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Bistability in a hyperchaotic system with a line equilibrium |
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| Authors: | Chunbiao Li J C Sprott Wesley Thio |
| Institution: | 1. School of Information Science and Engineering, Southeast University, Nanjing, 210096, China 2. Department of Physics, University of Wisconsin-Madison, Madison, WI, 53706, USA 4. Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing, 210007, China 3. Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, 43210, USA |
| Abstract: | 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. |
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