Periodic occurrence of chaotic behavior of homoclinic tangles
type: Item
instance of: scholarly article
title: Periodic occurrence of chaotic behavior of homoclinic tangles
zbMATH Open document ID: 1191.37015
published in: Physica D
publication date: 2010-04-21T00:00:00Z
review text: The article deals with numerical simulations of some important aspects of the dynamics of the periodically perturbed homoclinic solutions for the following differential equations \[ \frac{d^2q}{dt^2} + (\lambda - \gamma q^2) \frac{dq}{dt} - q + q^2 = 0; \] in other words, the solutions to the equation \[ \frac{d^2q}{dt^2} + (\lambda - \gamma q^2) \frac{dq}{dt} - q + q^2 = \mu \sin \omega t \] with a small \(\mu\) are studied. The article is written in the descriptive manner; it presents only tables and graphs demonstrating the creation of homoclinic tangles and some accompanying effects (horseshoes, periodic sinks, attractors, stable and unstable manifolds, and so on). There are no theorems, proofs, or sound reasoning validating the corresponding effects mentioned above.
Mathematics Subject Classification ID: 37C40
Mathematics Subject Classification ID: 37J45
zbMATH DE Number: 5696551
zbMATH Keywords: chaos
zbMATH Keywords: dissipative saddle
author: Qiudong Wang
author: Ali Oksasoglu
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
full work available at URL: j.physd.2009.12.006
OpenAlex ID: W1983319635
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DOI: 10.1016/J.PHYSD.2009.12.006
description: scientific article; zbMATH DE number 5696551