Pham VT, Gokul P.M., Kapitaniak T., Volos C, Azar AT (2018) Dynamics, Synchronization and Fractional Order Form of a Chaotic System With Infinite Equilibria. In: Mathematical Techniques of Fractional Order Systems, Advances in Nonlinear Dynamics and Chaos (ANDC) series, pp. 475–502, Elsevier
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Conventional chaotic systems, such as the Lorenz system, Rössler system, Chen system, or Lü system, have a countable number of equilibrium points. Interestingly, a few unusual systems with infinite equilibria have been discovered recently. It is worth noting that from a computational point of view, that equilibria cannot support to identify the attractors in such systems. This chapter presents a three-dimensional chaotic system with an infinite number of equilibrium points. The fundamental properties of such a system are investigated by using equilibrium analysis, phase portraits, Poincaré map, bifurcation diagram, and Lyapunov exponents. Interestingly, the system with infinite equilibria exhibits coexisting attractors. Chaos synchronization ability of the proposed system is studied via adaptive control. In addition, a fractional order form of the new system is also reported.