Asymmetric Bistability in the Rössler System

Julien Clinton Sprott
Department of Physics, University of Wisconsin–Madison
Madison, WI 53706, USA

Chunbiao Li
Jiangsu Key Laboratory of Meteorological Observation
and Information Processing
Nanjing University of Information Science & Technology
Nanjing 210044, China
School of Electronic & Information Engineering
Nanjing University of Information Science & Technology
Nanjing 210044, China

(Received October 21, 2016; accepted January 2, 2017)


Symmetric pairs of coexisting attractors are commonly found in symmetric dynamical systems when symmetry breaking occurs. By contrast, asymmetric bistability is rarely reported in either symmetric or asymmetric dynamical systems because such behavior typically occurs in narrow regions of parameter space and thus is often unnoticed. This paper describes an exploration of the regular parameter space of the Rössler system and shows examples of strange attractors coexisting with other strange attractors and with limit cycles, and asymmetric pairs of limit cycles in limited parameter space. A particular 1D path through parameter space is chosen to illustrate the various regions and the bifurcations that accompany the birth and death of the coexisting asymmetric attractors.

Ref: J. C. Sprott and C. Li, Acta Physica Polonica B 32, 97-107 (2017)

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