stochasticTipping

Class SingleLeakyIntegratorWithIntrinsicPlasticityAndNoiseInputODE

java.lang.Object

stochasticTipping.SingleLeakyIntegratorWithIntrinsicPlasticityAndNoiseInputODE

All Implemented Interfaces:

org.apache.commons.math3.ode.FirstOrderDifferentialEquations

public class SingleLeakyIntegratorWithIntrinsicPlasticityAndNoiseInputODE
extends java.lang.Object
implements org.apache.commons.math3.ode.FirstOrderDifferentialEquations

This class implements a single leaky integrator with intrinsic plasticity and noise driving. It is used in the class @see SingleLeakyIntegratorWithIntrinsicPlasticityAndNoiseInputODE in order to reproduce the results from the scientific article "Self-organized stochastic tipping in slow-fast dynamical systems" by Mathias Linkerhand and Claudius Gros.

Since:

2012

Constructor Summary

Constructors

Constructor and Description
SingleLeakyIntegratorWithIntrinsicPlasticityAndNoiseInputODE(double gamma, double w, double epsilon_a, double epsilon_b, double lambda_1, double lambda_2, double tNoiseConstantInterval, double xi_min, double xi_max) Creates a new leaky integrator with random noise input according to the specified parameters.

Method Summary

Methods

Modifier and Type	Method and Description
void	computeDerivatives(double time, double[] state, double[] stateDot) Calculates the first derivatives of the ODE.
static double	g(double x, double a, double b) Transfer function $g(x, a, b) = \frac{1}{1 + e^{-a(x-b)}}$.
int	getDimension() Returns the dimension of the ODE.
double	randomWhiteNoiseWithConstantTableaus(double t, double tNoiseConstantInterval, double xi_min, double xi_max) Random white noise with constant tableaus.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SingleLeakyIntegratorWithIntrinsicPlasticityAndNoiseInputODE

public SingleLeakyIntegratorWithIntrinsicPlasticityAndNoiseInputODE(double gamma,
                                                            double w,
                                                            double epsilon_a,
                                                            double epsilon_b,
                                                            double lambda_1,
                                                            double lambda_2,
                                                            double tNoiseConstantInterval,
                                                            double xi_min,
                                                            double xi_max)

Creates a new leaky integrator with random noise input according to the specified parameters.

Parameters:

gamma - leak

w - weighted adjacency matrix

epsilon_a - transfer function gain learning rate

epsilon_b - transfer function threshold learning rate

lambda_1 - target firing rate distribution parameter 1

lambda_2 - target firing rate distribution parameter 2

Method Detail

getDimension

public int getDimension()

Returns the dimension of the ODE.

Specified by:

getDimension in interface org.apache.commons.math3.ode.FirstOrderDifferentialEquations

Returns:

3

computeDerivatives

public void computeDerivatives(double time,
                      double[] state,
                      double[] stateDot)

Calculates the first derivatives of the ODE.

Specified by:

computeDerivatives in interface org.apache.commons.math3.ode.FirstOrderDifferentialEquations

Parameters:

time - time $t$

state - vector $(x(t), a(t), b(t))$

stateDot - vector $(\dot{x}(t), \dot{a}(t), \dot{b}(t))$

g

public static double g(double x,
       double a,
       double b)

Transfer function $g(x, a, b) = \frac{1}{1 + e^{-a(x-b)}}$.

Parameters:

x - membrane potential $x$

a - transfer function gain $a$

b - transfer function threshold $b$

Returns:

firing rate $y = g(x, a, b)$

randomWhiteNoiseWithConstantTableaus

public double randomWhiteNoiseWithConstantTableaus(double t,
                                          double tNoiseConstantInterval,
                                          double xi_min,
                                          double xi_max)

Random white noise with constant tableaus. The noise remains constant for $\delta t = 1$. This functions works only if called with increasing parameter t. Random access would give wrong results.

Parameters:

t - time

Returns:

random value of the corresponding plateau