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A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

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  • Viet-Thanh Pham
  • Christos Volos
  • Sundarapandian Vaidyanathan
  • Xiong Wang

Abstract

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.

Suggested Citation

  • Viet-Thanh Pham & Christos Volos & Sundarapandian Vaidyanathan & Xiong Wang, 2016. "A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:4024836
    DOI: 10.1155/2016/4024836
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    References listed on IDEAS

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    1. Sun, Junwei & Guo, Jinchao & Yang, Cunxiang & Zheng, Anping & Zhang, Xuncai, 2015. "Adaptive generalized hybrid function projective dislocated synchronization of new four-dimensional uncertain chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 304-314.
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