# 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

- which functions the user has to provide and how to put them into the structure
`funcs`(demo1_funcs.html) - continuation of equilibria in a single parameter, demo1_stst.html
- computation of their stability (eigenvalues of linearization), demo1_stst.html
- continuation of Hopf bifurcations in two parameters (demo1_hopf.html)
- computation of normal form coefficients for Hopf bifurcations (to check if they are supercritical or subcritical), and of normal form coefficients for codimension-two bifurcations encountered along Hopf curves (demo1_normalforms.html),
- branching off from a Hopf bifurcation to continue a family of periodic orbits in a single parameter demo1_psol.html
- computation of stability of periodic orbits (Floquet multipliers of linearization) demo1_psol.html
- continuation of homoclinic connections in two parameters demo1_hcli.html
- continuation of folds of periodic orbits in two parameters demo1_POfold.html

## Contents

## Differential equations

The differential equations for this example are

This system models two coupled neurons with time delayed connections. It has two components ( and ), three delays (, and ), and four other parameters (, , and ).

The primary bifurcation parameter will be the second parameter is .

clear; % clear variables format compact close all; % close figures addpath('../../ddebiftool/'); % add ddebiftool folder to path %#ok<*ASGLU,*NOPTS,*NASGU>