Configurations of periodic orbits for equations with delayed positive feedback

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Vas, Gabriella¹ 

[1] Univ Szeged, Bolyai Inst, MTA SZTE Anal & Stochast Res Grp, 1 Aradi V Tere, Szeged, Hungary

关键词: Delay differential equation;    Positive feedback;    Large-amplitude periodic solution;    Slow oscillation;    Floquet multiplier;   

DOI  :  10.1016/j.jde.2016.10.031

来源: Elsevier

【 摘 要 】

We consider scalar delay differential equations of the form (x) over circle (t) = -mu x(t) + f (x(t-1)), where mu > 0 and f is a nondecreasing C-1-function. If chi is a fixed point of f(mu), : R there exists U -> f(u)/mu is an element of R with f(mu)(')(chi) > 1, then [-1, 0] there exists s ->chi is an element of R is an unstable equilibrium. A periodic solution is said to have large amplitude if it oscillates about at least two fixed points chi- < chi+ of f mu. with f(mu)(')(chi-) > 1 and f(mu)(')(chi+) > 1. We investigate what type of large -amplitude periodic solutions may exist at the same time when the number of such fixed points (and hence the number of unstable equilibria) is an arbitrary integer N >= 2. It is shown that the number of different configurations equals the number of ways in which N symbols can be parenthesized. The location of the Floquet multipliers of the corresponding periodic orbits is also discussed. (C) 2016 Elsevier Inc. All rights reserved.

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