Strange nonchaotic attractors in a family of quasiperiodically forced piecewise linear maps

Denghui Li, Zhengbang Cao* (Corresponding Author), Xiaoming Zhang, Celso Grebogi, Jianhua Xie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, a family of quasiperiodically forced piecewise linear maps is considered. We prove that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents are nonpositive, a necessary condition for the existence of a strange nonchaotic attractor.
Original languageEnglish
JournalInternational Journal of Bifurcation and Chaos
Publication statusAccepted/In press - 2 Jan 2021

Keywords

  • strange nonchaotic attractors
  • skew product map
  • invariant graph

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