Multistability and arithmetically period-adding bifurcations in piecewise smooth dynamical systems

Younghae Do, Ying-Cheng Lai

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Multistability has been a phenomenon of continuous interest in nonlinear dynamics. Most existing works so far have focused on smooth dynamical systems. Motivated by the fact that nonsmooth dynamical systems can arise commonly in realistic physical and engineering applications such as impact oscillators and switching electronic circuits, we investigate multistability in such systems. In particular, we consider a generic class of piecewise smooth dynamical systems expressed in normal form but representative of nonsmooth systems in realistic situations, and focus on the weakly dissipative regime and the Hamiltonian limit. We find that, as the Hamiltonian limit is approached, periodic attractors can be generated through a series of saddle-node bifurcations. A striking phenomenon is that the periods of the newly created attractors follow an arithmetic sequence. This has no counterpart in smooth dynamical systems. We provide physical analyses, numerical computations, and rigorous mathematical arguments to substantiate the finding.

Original languageEnglish (US)
Article number043107
JournalChaos
Volume18
Issue number4
DOIs
StatePublished - 2008

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Multistability
Nonlinear Dynamics
Bifurcation (mathematics)
dynamical systems
Dynamical systems
Bifurcation
Dynamical system
Hamiltonians
Attractor
Switching circuits
Saddle-node Bifurcation
Arithmetic sequence
saddles
Engineering Application
Numerical Computation
Normal Form
oscillators
Electronics
engineering
Series

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Medicine(all)

Cite this

Multistability and arithmetically period-adding bifurcations in piecewise smooth dynamical systems. / Do, Younghae; Lai, Ying-Cheng.

In: Chaos, Vol. 18, No. 4, 043107, 2008.

Research output: Contribution to journalArticle

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