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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.

Coexistence of synchronization and anti-synchronization in chaotic systems

Ren L., Guo R., Vincent U. E.

Archives of Control Sciences

2016

Vol. 26, no. 1

69--79

The coexistence of anti-synchronization and synchronization in chaotic systems is investigated. A novel algorithm is proposed to determine the variables of the master system that should anti-synchronize with corresponding variables of the slave system. Control strategies that guarantee the coexistence of synchronization and anti-synchronization in the unified chaotic system are presented; while numerical simulations are employed to validate and illustrate the effectiveness of the proposed method.

Anti-synchronization in different new chaotic systems via active nonlinear control

Khan A., Prasad R. P.

Archives of Control Sciences

2013

Vol. 23, no. 2

229-242

In this paper, we discuss anti-synchronization between two identical new chaotic systems and anti-synchronization between another two identical new chaotic systems by active nonlinear control. The sufficient conditions for achieving the anti-synchronization of two new chaotic systems are derived based on Lyapunov stability theory. Numerical simulations are provided for illustration and verification of the proposed method.