A characteristic frequency of chaotic dynamical system
type: Item
instance of: scholarly article
title: A characteristic frequency of chaotic dynamical system
zbMATH Open document ID: 0794.34030
DOI: 10.1016/0960-0779(93)90048-6
published in: Chaos, Solitons and Fractals
publication date: 1994-05-08T00:00:00Z
review text: Headline's characteristic frequency is the frequency of a periodical external force which -- having a sufficiently large amplitude -- can synchronise a chaotic motion. Author's heuristic idea is: using the concept of ``analytical signal'' and a computed (or measured) solution of a chaotic motion this characteristic frequency can be calculated easily supposing this is the most probable ``instantaneous frequency'' of the solution. Examination of this assumption is carried out on two well-known systems: the Chua and the Lorenz system. Physical mechanism of oscillation excitation is considered different of these systems and therefore hoped the result will be sufficiently general. Synchronisation regions of the Chua oscillator were found numerically; one of these regions is near to a frequency calculated with the aid of the corresponding linear system; another region is in the vicinity of the most probable instantaneous frequency calculated according to author's suppositions. The author tries to apply his assumption for a periodically driven nonlinear oscillator, the Duffing one, executing chaotic oscillations. Calculating the most probable instantaneous frequency and inserting another external force with this frequency an amplitude threshold was found above which synchronisation of the chaotic oscillations occured. The author hopes this characteristic frequency can be useful for monitoring and diagnosis of certain dynamical systems.
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 558820
zbMATH Keywords: characteristic frequency
zbMATH Keywords: chaotic motion
zbMATH Keywords: Lorenz system
zbMATH Keywords: Chua oscillator
zbMATH Keywords: periodically driven nonlinear oscillator
zbMATH Keywords: Duffing
zbMATH Keywords: chaotic oscillations
zbMATH Keywords: synchronisation
zbMATH Keywords: dynamical systems
author: Michael Rosenblum
reviewed by: Á. P. Bosznay
MaRDI profile type: Publication
full work available at URL: 0960-0779(93)90048-6
OpenAlex ID: W2039349922
cites work: Synchronizing the chaotic oscillations by external force
cites work: Birth and death of the double scroll
cites work: Auto-oscillation Systems with Inertial Self-excitation
cites work: Q4004137
cites work: Controlling chaos
description: scientific article; zbMATH DE number 558820