Dynamics and circuit of a chaotic system with a curve of equilibrium points

ABSTRACT

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones.

KEYWORDS:

• Chaos
• attractor
• equilibrium
• coexisting attractors
• electronic circuit

Acknowledgements

The authors would like to thank the editor and reviewers for their invaluable comments to improve this work. The authors acknowledge Prof. GuanRong Chen, Department of Electronic Engineering, City University of Hong Kong, for suggesting many helpful references.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the Polish National Science Centre, MAESTRO Programme [Project No. 2013/08/A/ST8/00/780]. The author Xiong Wang was supported by the National Natural Science Foundation of China [No. 61601306] and Shenzhen Overseas High Level Talent Peacock Project Fund [No. 20150215145C]; National Natural Science Foundation of China [No. 61601306];Polish National Science Centre [MAESTRO Programme Project No. 2013/08/A/ST8/00/780]; Shenzhen Overseas High Level Talent Peacock Project Fund [No. 20150215145C].