Dynamics of a Delay Differential Equation with Multiple State-dependent Delays

@inproceedings{Humphries2011DynamicsOA,
title={Dynamics of a Delay Differential Equation with Multiple State-dependent Delays},
author={A. R. Humphries and Finn Upham},
year={2011}
}

We study the dynamics of a linear scalar delay differential equation εu̇(t) = −γu(t) − N ∑ i=1 κiu(t− ai − ciu(t)), which has trivial dynamics with fixed delays (ci = 0). We show that if the delays are allowed to be linearly state-dependent (ci 6= 0) then very complex dynamics can arise, when there are two or more delays. We present a numerical study of the bifurcation structures that arise in the dynamics, in the nonsingularly perturbed case, ε = 1. We concentrate on the case N = 2 and c1 = c2… CONTINUE READING