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Basins of attraction in forced systems with time-varying dissipation

Wright, JA, Deane, JHB, Bartuccelli, M and Gentile, G (2014) Basins of attraction in forced systems with time-varying dissipation Communications in Nonlinear Science and Numerical Simulation 29 (2015), 72-87, 29 (1-3). pp. 72-87.

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Abstract

We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final value. First, we consider situations where one is interested in the basins of attraction for damping coefficients varying linearly between two given values over many different time intervals: we outline a method to reduce the computation time required to estimate numerically the relative areas of the basins and discuss its range of applicability. Second, we observe that sometimes very slight changes in the time interval may produce abrupt large variations in the relative areas of the basins of attraction of the surviving attractors: we show how comparing the contracted phase space at a time after the final value of dissipation has been reached with the basins of attraction corresponding to that value of constant dissipation can explain the presence of such variations. Both procedures are illustrated by application to a pendulum with periodically oscillating support.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Wright, JAUNSPECIFIEDUNSPECIFIED
Deane, JHBUNSPECIFIEDUNSPECIFIED
Bartuccelli, MUNSPECIFIEDUNSPECIFIED
Gentile, GUNSPECIFIEDUNSPECIFIED
Date : 2 July 2014
Uncontrolled Keywords : Attractors, Basins of attraction, Forced systems, Dissipative systems, Damping coefficient, Non-constant dissipation, Pendulum with oscillating support
Related URLs :
Additional Information : This is the author's version of a paper submitted to Elsevier, and available at http://arxiv.org/abs/1407.0556v1
Depositing User : Symplectic Elements
Date Deposited : 28 Nov 2014 10:54
Last Modified : 15 Jul 2016 13:41
URI: http://epubs.surrey.ac.uk/id/eprint/806740

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