Chaotic behavior of a class of nonlinear differential delay equations
type: Item
instance of: scholarly article
title: Chaotic behavior of a class of nonlinear differential delay equations
zbMATH Open document ID: 0568.34057
DOI: 10.1007/BF01762537
author: Hans-Willi Siegberg
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1984-01-01T00:00:00Z
review text: The author studies the chaotic behavior, in the sense of Li and Yorke, for a class of nonlinear differential delay equations of the type \(x'(t)=-f_{\mu}(x(t-1)),\) where \(f_{\mu}: R\to R\) is a continuous odd function satisfying (i) \(f_{\mu}(x)=\mu\), for \(\delta <x<1-\delta\), (ii) \(f_{\mu}(x)=sign(x)\), for \(| x| \geq 1\), (iii) \(f_{\mu}(x)=-\mu\), for \(\delta -1<x<-\delta\), and (iv) \(\mu\in (2,3)\), \(0<\delta \ll 1/2\). In particular, he proves that the equation has infinitely many periodic as well as infinitely many aperiodic solutions.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 3906933
zbMATH Keywords: chaotic behavior
zbMATH Keywords: nonlinear differential delay equations
MaRDI profile type: Publication
cites work: Stability of Periodic Orbits in the Theorem of Sarkovskii
cites work: Periodic points and chaotic functions in the unit interval
cites work: Q3908199
cites work: Period Three Implies Chaos
cites work: Snap-back repellers imply chaos in \(\mathbb{R}^n\)
cites work: Simple mathematical models with very complicated dynamics
cites work: Periodic solutions of some nonlinear autonomous functional differential equations
cites work: Uniqueness and nonuniqueness of periodic solutions of x'(t)= -g(x(t-1))
cites work: Q3874572
cites work: Chaotic behaviour of nonlinear differential-delay equations
cites work: Q4743672
cites work: Q5186439
cites work: Chaotic Difference Equations: Generic Aspects
cites work: Homoclinic solution and chaos in
full work available at URL: https://doi.org/10.1007/bf01762537
OpenAlex ID: W1986451150
description: scientific article; zbMATH DE number 3906933