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"""!
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@brief Oscillatory Neural Network based on Hodgkin-Huxley Neuron Model
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@details Based on article description:
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- D.Chik, R.Borisyuk, Y.Kazanovich. Selective attention model with spiking elements. 2009.
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@authors Andrei Novikov ([email protected])
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@date 2014-2016
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@copyright GNU Public License
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@cond GNU_PUBLIC_LICENSE
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PyClustering is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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PyClustering is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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@endcond
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"""
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from pyclustering.nnet import *;
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from scipy.integrate import odeint;
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from pyclustering.utils import allocate_sync_ensembles;
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import numpy;
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import random;
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class hhn_parameters:
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"""!
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@brief Describes parameters of Hodgkin-Huxley Oscillatory Network.
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@see hhn_network
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"""
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44
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45
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## Intrinsic noise.
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nu = random.random() * 2.0 - 1.0;
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47
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48
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## Maximal conductivity for sodium current.
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gNa = 120.0 * (1 + 0.02 * nu);
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50
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51
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## Maximal conductivity for potassium current.
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gK = 36.0 * (1 + 0.02 * nu);
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53
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54
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## Maximal conductivity for leakage current.
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gL = 0.3 * (1 + 0.02 * nu);
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## Reverse potential of sodium current [mV].
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vNa = 50.0;
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## Reverse potential of potassium current [mV].
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vK = -77.0;
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## Reverse potantial of leakage current [mV].
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vL = -54.4;
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67
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## Rest potential [mV].
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vRest = -65.0;
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## External current [mV] for central element 1.
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Icn1 = 5.0;
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## External current [mV] for central element 2.
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Icn2 = 30.0;
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77
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## Synaptic reversal potential [mV] for inhibitory effects.
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Vsyninh = -80.0;
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## Synaptic reversal potential [mV] for exciting effects.
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Vsynexc = 0.0;
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## Alfa-parameter for alfa-function for inhibitory effect.
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alfa_inhibitory = 6.0;
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## Betta-parameter for alfa-function for inhibitory effect.
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betta_inhibitory = 0.3;
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## Alfa-parameter for alfa-function for excitatoty effect.
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alfa_excitatory = 40.0;
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## Betta-parameter for alfa-function for excitatoty effect.
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betta_excitatory = 2.0;
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## Strength of the synaptic connection from PN to CN1.
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w1 = 0.1;
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## Strength of the synaptic connection from CN1 to PN.
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w2 = 9.0;
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## Strength of the synaptic connection from CN2 to PN.
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w3 = 5.0;
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## Period of time [ms] when high strength value of synaptic connection exists from CN2 to PN.
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deltah = 650.0;
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## Threshold of the membrane potential that should exceeded by oscillator to be considered as an active.
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threshold = -10;
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## Affects pulse counter.
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eps = 0.16;
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class central_element:
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"""!
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@brief Central element consist of two central neurons that are described by a little bit different dynamic than peripheral.
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@see hhn_network
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"""
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## Membrane potential of cenral neuron (V).
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membrane_potential = 0.0;
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## Activation conductance of the sodium channel (m).
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active_cond_sodium = 0.0;
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## Inactivaton conductance of the sodium channel (h).
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inactive_cond_sodium = 0.0;
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## Inactivaton conductance of the sodium channel (h)
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active_cond_potassium = 0.0;
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## Times of pulse generation by central neuron.
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pulse_generation_time = None;
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## Spike generation of central neuron.
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pulse_generation = False;
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def __init__(self):
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"""!
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@brief Constructor of central element.
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"""
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self.pulse_generation_time = [];
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def __repr__(self):
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"""!
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@brief Returns string that represents central element.
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"""
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return "%s, %s" % (self.membrane_potential, self.pulse_generation_time);
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class hhn_network(network):
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"""!
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@brief Oscillatory Neural Network with central element based on Hodgkin-Huxley neuron model. Interaction between oscillators is performed via
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central element (no connection between oscillators that are called as peripheral). Peripheral oscillators receive external stimulus.
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Central element consist of two oscillators: the first is used for synchronization some ensemble of oscillators and the second controls
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synchronization of the first cental oscillator with verious ensembles.
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Example:
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@code
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# change period of time when high strength value of synaptic connection exists from CN2 to PN.
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params = hhn_parameters();
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params.deltah = 400;
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# create oscillatory network with stimulus
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net = hhn_network(6, [0, 0, 25, 25, 47, 47], params);
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# simulate network
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(t, dyn) = net.simulate(1200, 600);
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# draw network output during simulation
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draw_dynamics(t, dyn, x_title = "Time", y_title = "V", separate = True);
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@endcode
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"""
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_name = "Oscillatory Neural Network based on Hodgkin-Huxley Neuron Model"
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# States of peripheral oscillators
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_membrane_potential = None; # membrane potential of neuron (V)
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_active_cond_sodium = None; # activation conductance of the sodium channel (m)
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_inactive_cond_sodium = None; # inactivaton conductance of the sodium channel (h)
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_active_cond_potassium = None; # activation conductance of the potassium channel (n)
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_link_activation_time = None; # time of set w3 - connection from CN2 to PN for each oscillator.
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_link_weight3 = None; # connection strength for each oscillator from CN2 to PN.
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_pulse_generation_time = None; # time of spike generation for each oscillator.
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_pulse_generation = None; # spike generation for each oscillator.
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_stimulus = None; # stimulus of each oscillator
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_noise = None; # Noise for each oscillator
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_central_element = None; # Central element description
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_params = None; # parameters of the network
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_membrane_dynamic_pointer = None; # final result is stored here.
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def __init__(self, num_osc, stimulus = None, parameters = None, type_conn = None, type_conn_represent = conn_represent.MATRIX):
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"""!
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@brief Constructor of oscillatory network based on Hodgkin-Huxley meuron model.
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@param[in] num_osc (uint): Number of peripheral oscillators in the network.
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@param[in] stimulus (list): List of stimulus for oscillators, number of stimulus should be equal to number of peripheral oscillators.
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@param[in] parameters (hhn_parameters): Parameters of the network.
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@param[in] type_conn (conn_type): Type of connections between oscillators in the network (ignored for this type of network).
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@param[in] type_conn_represent (conn_represent): Internal representation of connection in the network: matrix or list.
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"""
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super().__init__(num_osc, conn_type.NONE, type_conn_represent);
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self._membrane_potential = [0.0] * self._num_osc;
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self._active_cond_sodium = [0.0] * self._num_osc;
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self._inactive_cond_sodium = [0.0] * self._num_osc;
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self._active_cond_potassium = [0.0] * self._num_osc;
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self._link_activation_time = [0.0] * self._num_osc;
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self._link_pulse_counter = [0.0] * self._num_osc;
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self._link_deactivation_time = [0.0] * self._num_osc;
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self._link_weight3 = [0.0] * self._num_osc;
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self._pulse_generation_time = [ [] for i in range(self._num_osc) ];
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self._pulse_generation = [False] * self._num_osc;
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self._noise = [random.random() * 2.0 - 1.0 for i in range(self._num_osc)];
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234
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self._central_element = [central_element(), central_element()];
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if (stimulus is None):
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self._stimulus = [0.0] * self._num_osc;
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else:
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self._stimulus = stimulus;
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if (parameters is not None):
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self._params = parameters;
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else:
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self._params = hhn_parameters();
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def simulate(self, steps, time, solution = solve_type.RK4, collect_dynamic = True):
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"""!
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@brief Performs static simulation of oscillatory network based on Hodgkin-Huxley neuron model.
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@param[in] steps (uint): Number steps of simulations during simulation.
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@param[in] time (double): Time of simulation.
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@param[in] solution (solve_type): Type of solver for differential equations.
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@param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
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256
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@return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,
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otherwise returns only last values (last step of simulation) of dynamic.
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"""
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return self.simulate_static(steps, time, solution, collect_dynamic);
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263
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264
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def simulate_static(self, steps, time, solution = solve_type.RK4, collect_dynamic = False):
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"""!
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266
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@brief Performs static simulation of oscillatory network based on Hodgkin-Huxley neuron model.
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268
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@param[in] steps (uint): Number steps of simulations during simulation.
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@param[in] time (double): Time of simulation.
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270
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@param[in] solution (solve_type): Type of solver for differential equations.
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271
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@param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
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272
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273
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@return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,
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otherwise returns only last values (last step of simulation) of dynamic.
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275
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276
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"""
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277
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278
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self._membrane_dynamic_pointer = None;
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279
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280
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# Check solver before simulation
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if (solution == solve_type.FAST):
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raise NameError("Solver FAST is not support due to low accuracy that leads to huge error.");
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283
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elif (solution == solve_type.RKF45):
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284
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raise NameError("Solver RKF45 is not support in python version.");
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285
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286
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dyn_memb = None;
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287
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dyn_time = None;
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288
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289
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# Store only excitatory of the oscillator
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290
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if (collect_dynamic == True):
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291
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dyn_memb = [];
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292
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dyn_time = [];
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293
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294
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step = time / steps;
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295
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int_step = step / 10.0;
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296
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|
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|
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297
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|
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for t in numpy.arange(step, time + step, step):
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298
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# update states of oscillators
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299
|
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memb = self._calculate_states(solution, t, step, int_step);
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300
|
|
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301
|
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# update states of oscillators
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302
|
|
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if (collect_dynamic == True):
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303
|
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|
dyn_memb.append(memb);
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304
|
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dyn_time.append(t);
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305
|
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else:
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306
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dyn_memb = memb;
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307
|
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dyn_time = t;
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308
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|
|
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309
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self._membrane_dynamic_pointer = dyn_memb;
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310
|
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return (dyn_time, dyn_memb);
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311
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312
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313
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def _calculate_states(self, solution, t, step, int_step):
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314
|
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|
"""!
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315
|
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|
@brief Caclculates new state of each oscillator in the network. Returns only excitatory state of oscillators.
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316
|
|
|
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317
|
|
|
@param[in] solution (solve_type): Type solver of the differential equations.
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318
|
|
|
@param[in] t (double): Current time of simulation.
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319
|
|
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@param[in] step (uint): Step of solution at the end of which states of oscillators should be calculated.
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320
|
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|
@param[in] int_step (double): Differentiation step that is used for solving differential equation.
|
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321
|
|
|
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322
|
|
|
@return (list) New states of membrance potentials for peripheral oscillators and for cental elements as a list where
|
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323
|
|
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the last two values correspond to central element 1 and 2.
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324
|
|
|
|
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325
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|
"""
|
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326
|
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|
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327
|
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next_membrane = [0.0] * self._num_osc;
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328
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next_active_sodium = [0.0] * self._num_osc;
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329
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|
next_inactive_sodium = [0.0] * self._num_osc;
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330
|
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|
next_active_potassium = [0.0] * self._num_osc;
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|
331
|
|
|
|
|
332
|
|
|
# Update states of oscillators
|
|
333
|
|
|
for index in range (0, self._num_osc, 1):
|
|
334
|
|
|
result = odeint(self.hnn_state,
|
|
335
|
|
|
[ self._membrane_potential[index], self._active_cond_sodium[index], self._inactive_cond_sodium[index], self._active_cond_potassium[index] ],
|
|
336
|
|
|
numpy.arange(t - step, t, int_step),
|
|
337
|
|
|
(index , ));
|
|
338
|
|
|
|
|
339
|
|
|
[ next_membrane[index], next_active_sodium[index], next_inactive_sodium[index], next_active_potassium[index] ] = result[len(result) - 1][0:4];
|
|
340
|
|
|
|
|
341
|
|
|
next_cn_membrane = [0.0, 0.0];
|
|
342
|
|
|
next_cn_active_sodium = [0.0, 0.0];
|
|
343
|
|
|
next_cn_inactive_sodium = [0.0, 0.0];
|
|
344
|
|
|
next_cn_active_potassium = [0.0, 0.0];
|
|
345
|
|
|
|
|
346
|
|
|
# Update states of central elements
|
|
347
|
|
|
for index in range(0, len(self._central_element)):
|
|
348
|
|
|
result = odeint(self.hnn_state,
|
|
349
|
|
|
[ self._central_element[index].membrane_potential, self._central_element[index].active_cond_sodium, self._central_element[index].inactive_cond_sodium, self._central_element[index].active_cond_potassium ],
|
|
350
|
|
|
numpy.arange(t - step, t, int_step),
|
|
351
|
|
|
(self._num_osc + index , ));
|
|
352
|
|
|
|
|
353
|
|
|
[ next_cn_membrane[index], next_cn_active_sodium[index], next_cn_inactive_sodium[index], next_cn_active_potassium[index] ] = result[len(result) - 1][0:4];
|
|
354
|
|
|
|
|
355
|
|
|
# Noise generation
|
|
356
|
|
|
self._noise = [ 1.0 + 0.01 * (random.random() * 2.0 - 1.0) for i in range(self._num_osc)];
|
|
357
|
|
|
|
|
358
|
|
|
# Updating states of PNs
|
|
359
|
|
|
self.__update_peripheral_neurons(t, step, next_membrane, next_active_sodium, next_inactive_sodium, next_active_potassium);
|
|
360
|
|
|
|
|
361
|
|
|
# Updation states of CN
|
|
362
|
|
|
self.__update_central_neurons(t, next_cn_membrane, next_cn_active_sodium, next_cn_inactive_sodium, next_cn_active_potassium);
|
|
363
|
|
|
|
|
364
|
|
|
return next_membrane + next_cn_membrane;
|
|
365
|
|
|
|
|
366
|
|
|
|
|
367
|
|
|
def __update_peripheral_neurons(self, t, step, next_membrane, next_active_sodium, next_inactive_sodium, next_active_potassium):
|
|
368
|
|
|
"""!
|
|
369
|
|
|
@brief Update peripheral neurons in line with new values of current in channels.
|
|
370
|
|
|
|
|
371
|
|
|
@param[in] t (doubles): Current time of simulation.
|
|
372
|
|
|
@param[in] step (uint): Step (time duration) during simulation when states of oscillators should be calculated.
|
|
373
|
|
|
@param[in] next_membrane (list): New values of membrane potentials for peripheral neurons.
|
|
374
|
|
|
@Param[in] next_active_sodium (list): New values of activation conductances of the sodium channels for peripheral neurons.
|
|
375
|
|
|
@param[in] next_inactive_sodium (list): New values of inactivaton conductances of the sodium channels for peripheral neurons.
|
|
376
|
|
|
@param[in] next_active_potassium (list): New values of activation conductances of the potassium channel for peripheral neurons.
|
|
377
|
|
|
|
|
378
|
|
|
"""
|
|
379
|
|
|
|
|
380
|
|
|
self._membrane_potential = next_membrane[:];
|
|
381
|
|
|
self._active_cond_sodium = next_active_sodium[:];
|
|
382
|
|
|
self._inactive_cond_sodium = next_inactive_sodium[:];
|
|
383
|
|
|
self._active_cond_potassium = next_active_potassium[:];
|
|
384
|
|
|
|
|
385
|
|
|
for index in range(0, self._num_osc):
|
|
386
|
|
|
if (self._pulse_generation[index] is False):
|
|
387
|
|
|
if (self._membrane_potential[index] > 0.0):
|
|
388
|
|
|
self._pulse_generation[index] = True;
|
|
389
|
|
|
self._pulse_generation_time[index].append(t);
|
|
390
|
|
|
else:
|
|
391
|
|
|
if (self._membrane_potential[index] < 0.0):
|
|
392
|
|
|
self._pulse_generation[index] = False;
|
|
393
|
|
|
|
|
394
|
|
|
# Update connection from CN2 to PN
|
|
395
|
|
|
if (self._link_weight3[index] == 0.0):
|
|
396
|
|
|
if ( (self._membrane_potential[index] > self._params.threshold) and (self._membrane_potential[index] > self._params.threshold) ):
|
|
397
|
|
|
self._link_pulse_counter[index] += step;
|
|
398
|
|
|
|
|
399
|
|
|
if (self._link_pulse_counter[index] >= 1 / self._params.eps):
|
|
400
|
|
|
self._link_weight3[index] = self._params.w3;
|
|
401
|
|
|
self._link_activation_time[index] = t;
|
|
402
|
|
|
else:
|
|
403
|
|
|
if ( not ((self._link_activation_time[index] < t) and (t < self._link_activation_time[index] + self._params.deltah)) ):
|
|
404
|
|
|
self._link_weight3[index] = 0.0;
|
|
405
|
|
|
self._link_pulse_counter[index] = 0.0;
|
|
406
|
|
|
|
|
407
|
|
|
|
|
408
|
|
|
def __update_central_neurons(self, t, next_cn_membrane, next_cn_active_sodium, next_cn_inactive_sodium, next_cn_active_potassium):
|
|
409
|
|
|
"""!
|
|
410
|
|
|
@brief Update of central neurons in line with new values of current in channels.
|
|
411
|
|
|
|
|
412
|
|
|
@param[in] t (doubles): Current time of simulation.
|
|
413
|
|
|
@param[in] next_membrane (list): New values of membrane potentials for central neurons.
|
|
414
|
|
|
@Param[in] next_active_sodium (list): New values of activation conductances of the sodium channels for central neurons.
|
|
415
|
|
|
@param[in] next_inactive_sodium (list): New values of inactivaton conductances of the sodium channels for central neurons.
|
|
416
|
|
|
@param[in] next_active_potassium (list): New values of activation conductances of the potassium channel for central neurons.
|
|
417
|
|
|
|
|
418
|
|
|
"""
|
|
419
|
|
|
|
|
420
|
|
|
for index in range(0, len(self._central_element)):
|
|
421
|
|
|
self._central_element[index].membrane_potential = next_cn_membrane[index];
|
|
422
|
|
|
self._central_element[index].active_cond_sodium = next_cn_active_sodium[index];
|
|
423
|
|
|
self._central_element[index].inactive_cond_sodium = next_cn_inactive_sodium[index];
|
|
424
|
|
|
self._central_element[index].active_cond_potassium = next_cn_active_potassium[index];
|
|
425
|
|
|
|
|
426
|
|
|
if (self._central_element[index].pulse_generation is False):
|
|
427
|
|
|
if (self._central_element[index].membrane_potential > 0.0):
|
|
428
|
|
|
self._central_element[index].pulse_generation = True;
|
|
429
|
|
|
self._central_element[index].pulse_generation_time.append(t);
|
|
430
|
|
|
else:
|
|
431
|
|
|
if (self._central_element[index].membrane_potential < 0.0):
|
|
432
|
|
|
self._central_element[index].pulse_generation = False;
|
|
433
|
|
|
|
|
434
|
|
|
|
|
435
|
|
|
def hnn_state(self, inputs, t, argv):
|
|
436
|
|
|
"""!
|
|
437
|
|
|
@brief Returns new values of excitatory and inhibitory parts of oscillator and potential of oscillator.
|
|
438
|
|
|
|
|
439
|
|
|
@param[in] inputs (list): States of oscillator for integration [v, m, h, n] (see description below).
|
|
440
|
|
|
@param[in] t (double): Current time of simulation.
|
|
441
|
|
|
@param[in] argv (tuple): Extra arguments that are not used for integration - index of oscillator.
|
|
442
|
|
|
|
|
443
|
|
|
@return (list) new values of oscillator [v, m, h, n], where:
|
|
444
|
|
|
v - membrane potantial of oscillator,
|
|
445
|
|
|
m - activation conductance of the sodium channel,
|
|
446
|
|
|
h - inactication conductance of the sodium channel,
|
|
447
|
|
|
n - activation conductance of the potassium channel.
|
|
448
|
|
|
|
|
449
|
|
|
"""
|
|
450
|
|
|
|
|
451
|
|
|
index = argv;
|
|
452
|
|
|
|
|
453
|
|
|
v = inputs[0]; # membrane potential (v).
|
|
454
|
|
|
m = inputs[1]; # activation conductance of the sodium channel (m).
|
|
455
|
|
|
h = inputs[2]; # inactivaton conductance of the sodium channel (h).
|
|
456
|
|
|
n = inputs[3]; # activation conductance of the potassium channel (n).
|
|
457
|
|
|
|
|
458
|
|
|
# Calculate ion current
|
|
459
|
|
|
# gNa * m[i]^3 * h * (v[i] - vNa) + gK * n[i]^4 * (v[i] - vK) + gL (v[i] - vL)
|
|
460
|
|
|
active_sodium_part = self._params.gNa * (m ** 3) * h * (v - self._params.vNa);
|
|
461
|
|
|
inactive_sodium_part = self._params.gK * (n ** 4) * (v - self._params.vK);
|
|
462
|
|
|
active_potassium_part = self._params.gL * (v - self._params.vL);
|
|
463
|
|
|
|
|
464
|
|
|
Iion = active_sodium_part + inactive_sodium_part + active_potassium_part;
|
|
465
|
|
|
|
|
466
|
|
|
Iext = 0.0;
|
|
467
|
|
|
Isyn = 0.0;
|
|
468
|
|
|
if (index < self._num_osc):
|
|
469
|
|
|
# PN - peripheral neuron - calculation of external current and synaptic current.
|
|
470
|
|
|
Iext = self._stimulus[index] * self._noise[index]; # probably noise can be pre-defined for reducting compexity
|
|
471
|
|
|
|
|
472
|
|
|
memory_impact1 = 0.0;
|
|
473
|
|
|
for i in range(0, len(self._central_element[0].pulse_generation_time)):
|
|
474
|
|
|
# TODO: alfa function shouldn't be calculated here (long procedure)
|
|
475
|
|
|
memory_impact1 += self.__alfa_function(t - self._central_element[0].pulse_generation_time[i], self._params.alfa_inhibitory, self._params.betta_inhibitory);
|
|
476
|
|
|
|
|
477
|
|
|
memory_impact2 = 0.0;
|
|
478
|
|
|
for i in range(0, len(self._central_element[1].pulse_generation_time)):
|
|
479
|
|
|
# TODO: alfa function shouldn't be calculated here (long procedure)
|
|
480
|
|
|
memory_impact2 += self.__alfa_function(t - self._central_element[1].pulse_generation_time[i], self._params.alfa_inhibitory, self._params.betta_inhibitory);
|
|
481
|
|
|
|
|
482
|
|
|
Isyn = self._params.w2 * (v - self._params.Vsyninh) * memory_impact1 + self._link_weight3[index] * (v - self._params.Vsyninh) * memory_impact2;
|
|
483
|
|
|
else:
|
|
484
|
|
|
# CN - central element.
|
|
485
|
|
|
central_index = index - self._num_osc;
|
|
486
|
|
|
if (central_index == 0):
|
|
487
|
|
|
Iext = self._params.Icn1; # CN1
|
|
488
|
|
|
|
|
489
|
|
|
memory_impact = 0.0;
|
|
490
|
|
|
for index_oscillator in range(0, self._num_osc):
|
|
491
|
|
|
for index_generation in range(0, len(self._pulse_generation_time[index_oscillator])):
|
|
492
|
|
|
# TODO: alfa function shouldn't be calculated here (long procedure)
|
|
493
|
|
|
memory_impact += self.__alfa_function(t - self._pulse_generation_time[index_oscillator][index_generation], self._params.alfa_excitatory, self._params.betta_excitatory);
|
|
494
|
|
|
|
|
495
|
|
|
Isyn = self._params.w1 * (v - self._params.Vsynexc) * memory_impact;
|
|
496
|
|
|
|
|
497
|
|
|
elif (central_index == 1):
|
|
498
|
|
|
Iext = self._params.Icn2; # CN2
|
|
499
|
|
|
Isyn = 0.0;
|
|
500
|
|
|
|
|
501
|
|
|
else:
|
|
502
|
|
|
assert 0;
|
|
503
|
|
|
|
|
504
|
|
|
|
|
505
|
|
|
# Membrane potential
|
|
506
|
|
|
dv = -Iion + Iext - Isyn;
|
|
507
|
|
|
|
|
508
|
|
|
# Calculate variables
|
|
509
|
|
|
potential = v - self._params.vRest;
|
|
510
|
|
|
am = (2.5 - 0.1 * potential) / (math.exp(2.5 - 0.1 * potential) - 1.0);
|
|
511
|
|
|
ah = 0.07 * math.exp(-potential / 20.0);
|
|
512
|
|
|
an = (0.1 - 0.01 * potential) / (math.exp(1.0 - 0.1 * potential) - 1.0);
|
|
513
|
|
|
|
|
514
|
|
|
bm = 4.0 * math.exp(-potential / 18.0);
|
|
515
|
|
|
bh = 1.0 / (math.exp(3.0 - 0.1 * potential) + 1.0);
|
|
516
|
|
|
bn = 0.125 * math.exp(-potential / 80.0);
|
|
517
|
|
|
|
|
518
|
|
|
dm = am * (1.0 - m) - bm * m;
|
|
519
|
|
|
dh = ah * (1.0 - h) - bh * h;
|
|
520
|
|
|
dn = an * (1.0 - n) - bn * n;
|
|
521
|
|
|
|
|
522
|
|
|
return [dv, dm, dh, dn];
|
|
523
|
|
|
|
|
524
|
|
|
|
|
525
|
|
|
def allocate_sync_ensembles(self, tolerance = 0.1):
|
|
526
|
|
|
"""!
|
|
527
|
|
|
@brief Allocates clusters in line with ensembles of synchronous oscillators where each. Synchronous ensemble corresponds to only one cluster.
|
|
528
|
|
|
|
|
529
|
|
|
@param[in] tolerance (double): maximum error for allocation of synchronous ensemble oscillators.
|
|
530
|
|
|
|
|
531
|
|
|
@return (list) Grours (lists) of indexes of synchronous oscillators. For example [ [index_osc1, index_osc3], [index_osc2], [index_osc4, index_osc5] ].
|
|
532
|
|
|
|
|
533
|
|
|
"""
|
|
534
|
|
|
|
|
535
|
|
|
ignore = set();
|
|
536
|
|
|
|
|
537
|
|
|
ignore.add(self._num_osc);
|
|
538
|
|
|
ignore.add(self._num_osc + 1);
|
|
539
|
|
|
|
|
540
|
|
|
return allocate_sync_ensembles(self._membrane_dynamic_pointer, tolerance, 20.0, ignore);
|
|
541
|
|
|
|
|
542
|
|
|
|
|
543
|
|
|
def __alfa_function(self, time, alfa, betta):
|
|
544
|
|
|
"""!
|
|
545
|
|
|
@brief Calculates value of alfa-function for difference between spike generation time and current simulation time.
|
|
546
|
|
|
|
|
547
|
|
|
@param[in] time (double): Difference between last spike generation time and current time.
|
|
548
|
|
|
@param[in] alfa (double): Alfa parameter for alfa-function.
|
|
549
|
|
|
@param[in] betta (double): Betta parameter for alfa-function.
|
|
550
|
|
|
|
|
551
|
|
|
@return (double) Value of alfa-function.
|
|
552
|
|
|
|
|
553
|
|
|
"""
|
|
554
|
|
|
|
|
555
|
|
|
return alfa * time * math.exp(-betta * time);
|
|
556
|
|
|
|
annoviko /
pyclustering
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