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Advances in Mathematical Physics
Volume 2016, Article ID 4024836, 8 pages
Research Article

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

1School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam
2Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
3Research and Development Centre, Vel Tech University, Avadi, Chennai 600062, India
4Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, China

Received 27 September 2016; Accepted 14 November 2016

Academic Editor: Zhi-Yuan Sun

Copyright © 2016 Viet-Thanh Pham et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.