DYNAMICS OF A DELAY DIFFERENTIAL EQUATION WITH MULTIPLE STATE-DEPENDENT DELAYS

被引：15
|
作者：
Humphries, A. R. [1 ]
DeMasi, O. A. [1 ,2 ]
Magpantay, F. M. G. [1 ]
Upham, F. [1 ,3 ]
机构：
[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada
[2] Univ Calif Berkeley, Lawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
[3] NYU, Steinhardt Sch Culture Educ & Human Dev, New York, NY 10003 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2012年 / 32卷 / 08期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Delay differential equations; state-dependent delays; Hopf bifurcations; periodic solutions; bistability; tori; period-doubling; BOUNDARY-LAYER PHENOMENA; TIME LAGS; FEEDBACK; BISTABILITY;
D O I：
10.3934/dcds.2012.32.2701
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the dynamics of a linear scalar delay differential equationmm epsilon u(t) = -gamma u(t) - Sigma(N)(i=1)kappa(i)u(t - a(i) - c(i)u(t)), which has trivial dynamics with fixed delays (c(i) = 0). We show that if the delays are allowed to be linearly state-dependent (c(i) not equal 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 non-singularly perturbed case, epsilon = 1. We concentrate on the case N - 2 and c(1) = c(2) = c and show the existence of bistability of periodic orbits, stable invariant tori, isola of periodic orbits arising as locked orbits on the torus, and period doubling bifurcations.
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页码：2701 / 2727
页数：27
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