Analytical solutions of systems with piecewise linear dynamics

Y. Kominis; T. Bountis

doi:10.1142/S0218127410025570

Analytical solutions of systems with piecewise linear dynamics

Y. Kominis, T. Bountis

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.

Original language	English
Pages (from-to)	509-518
Number of pages	10
Journal	International Journal of Bifurcation and Chaos
Volume	20
Issue number	2
DOIs	https://doi.org/10.1142/S0218127410025570
Publication status	Published - Feb 2010

Keywords

Analytical solutions
Nonautonomous systems
Piecewise linear systems

ASJC Scopus subject areas

Modelling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

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AB - A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.

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