Bistability in a Hyperchaotic System with a Line Equilibrium

Chunbiao Lia, J.C.Sprottb, Wesley Thioc
aSchool of Information Science and Engineering, Southeast University 210096, Nanjing, China
bDepartment of Physics, University of Wisconsin-Madison 53706, Madison, WI, USA
cDepartment of Electrical and Computer Engineering, The Ohio State University 43210, Columbus, OH, USA
Received October 26, 2013

A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where the hyperchaos is largest is determined. In the vicinity of this point, different dynamics are observed including periodicity, quasi-periodicity, chaos, and hyperchaos. Under some conditions, the system has a unique bistable behavior, characterized by a symmetric pair of coexisting limit cycles that undergo period doubling, forming a symmetric pair of strange attractors that merge into a single symmetric chaotic attractor that then becomes hyperchaotic. The system was implemented as an electronic circuit whose behavior confirms the numerical predictions.

Ref: C. Li, J. C. Sprott, and W. Thio, Journal of Experimental and Theoretical Physics 118, 494-500 (2014)

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