DDE-BIFTOOL demo 1 - Neuron

(c) DDE-BIFTOOL v. 3.1.1(75), 31/12/2014

This demo is an illustrative example, which uses a system of delay differential equations taken from [Shay,99].

The demo will show


Differential equations

The differential equations for this example are

-\kappa x_1(t)+\beta \tanh(x_1(t-\tau_s))+a_{12}\tanh(x_2(t-\tau_2)) \\
\dot{x_2}(t)=-\kappa x_2(t)+\beta \tanh(x_2(t-\tau_s))+a_{21}\tanh(x_1(t-\tau_1)).

This system models two coupled neurons with time delayed connections. It has two components ($x_1$ and $x_2$), three delays ($\tau_1$, $\tau_2$ and $\tau_s$), and four other parameters ($\kappa$, $\beta$, $a_{12}$ and $a_{21}$).

The primary bifurcation parameter will be $a_{21}$ the second parameter is $\tau_s$.

clear;                           % clear variables
format compact
close all;                       % close figures
addpath('../../ddebiftool/');    % add ddebiftool folder to path

First step: the definition of user-defined functions, see demo1_funcs.html