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Coexisting of self-excited and hidden attractors in a new 4D hyperchaotic Sprott-S system with a single equilibrium point

Al-Azzawi Saad Fawzi, Al-Hayali Maryam A.

Archives of Control Sciences

2022

Vol. 32, No. 1

37--56

Coexisting self-excited and hidden attractors for the same set of parameters in dissipative dynamical systems are more interesting, important, and difficult compared to other classes of hidden attractors. By utilizing of nonlinear state feedback controller on the popular Sprott-S system to construct a new, unusual 4D system with only one nontrivial equilibrium point and two control parameters. These parameters affect system behavior and transformation from hidden attractors to self-excited attractors or vice versa. As compared to traditional similar kinds of systems with hidden attractors, this system is distinguished considering it has (𝑛-2) positive Lyapunov exponents with maximal Lyapunov exponent. In addition, the coexistence of multi-attractors and chaotic with 2-torus are found in the system through analytical results and experimental simulations which include equilibrium points, stability, phase portraits, and Lyapunov spectrum. Furthermore, the anti-synchronization realization of two identical new systems is done relying on Lyapunov stability theory and nonlinear controllers strategy. lastly, the numerical simulation confirmed the validity of the theoretical results.