Exploring hyperchaotic synchronization of a fractional-order system without equilibrium points: A sliding mode control approach

Iranian Journal of Numerical Analysis and Optimization

مقاله 4، دوره 15، Issue 2 - شماره پیاپی 33، شهریور 2025، صفحه 508-530   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.89779.1511

نویسندگان

R.A. Meskine؛ S. Kaouache^*

Laboratory of mathematics and their interactions, Department of Mathematics, Institute of Mathematics and Computer Science, Abdelhafid Boussouf University Center, Mila, Algeria.

چکیده

Recently, constructing hidden attractors of chaotic systems without equi-librium point has become a key discussion point in the application fields of chaos and hyperchaos science. This paper introduces a novel hyperchaotic system without equilibrium points, distinct from existing systems that rely on the Shilnikov criterion for demonstrating hyperchaos. This study inves-tigates the qualitative properties of the system, including its hyperchaotic attractors, Poincare map, Lyapunov exponents, and Kaplan-Yorke dimen-sion. To enhance the practical applicability of this system, an integral sliding mode control method for synchronization is proposed. Lyapunov theory ensures the stability and effectiveness of the synchronization scheme.The efficiency of the approach is demonstrated by numerical simulations, which validate the potential of the system for various applications.

کلیدواژه‌ها

Fractional derivative؛ Synchronization؛ Lyapunov stability theory؛ Lyapunov exponents؛ Sliding mode control

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