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

By Younghae Do and Ying-Cheng Lai

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Book Id: WPLBN0002169289
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 15 October 2008

Title: Chaos : Multistability and arithmetically period-adding bifurcations in piecewise smooth dynamical systems  
Author: Younghae Do and Ying-Cheng Lai
Volume: Issue : October 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection, Chaos Collection
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Publisher: American Institute of Physics

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And Ying-Cheng Lai, Y. D. (n.d.). Chaos : Multistability and arithmetically period-adding bifurcations in piecewise smooth dynamical systems. Retrieved from http://hawaiilibrary.net/


Description
Description: 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.

 

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