Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis

Iskakova K. Alam M.M. Ahmad S. Saifullah S. Akgül A. Yılmaz G.
June 2023 Elsevier B.V.

Mathematics and Computers in Simulation
2023 #208 219 - 245 pp.

In this article, a new nonlinear four-dimensional hyperchaotic model is presented. The dynamical aspects of the complex system are analyzed covering equilibrium points, linear stability, dissipation, bifurcations, Lyapunov exponent, phase portraits, Poincaré mapping, attractor projection, sensitivity and time series analysis. To analyze hidden attractors, the proposed system is investigated through nonlocal operator in Caputo sense. The existence of solution of the system in fractional sense is studied by fixed point theory. The stability of fractional order system is demonstrated via Matignon stability criteria. The fractional order system is numerically studied via newly developed numerical method which is based on Newton polynomial interpolation. The evolution of the attractors are depicted with different fractional orders. For few fractional orders, some hidden strange chaotic attractors are observed through graphs. Theoretical and numerical studies demonstrate that this model has complex dynamics with some stimulating physical characteristics. To verify and validate the results, we implement Field Programmable Analog Arrays (FPAA).

Bifurcations , Chaos , Lyapunov exponent , Newton polynomial , Poincaré mapping

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Department of Physics and Mathematics, Kazakh National Pedagogical University, Almaty, Kazakhstan
Department of Basic Medical Sciences, College of Applied Medical Science, King Khalid University, Abha, 61421, Saudi Arabia
Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Siirt University, Art and Science Faculty, Department of Mathematics, Siirt, TR-56100, Turkey
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey
Department of Electrical and Electronics Engineering, Erciyes University, Kayseri, Turkey

Department of Physics and Mathematics
Department of Basic Medical Sciences
Department of Mathematics
Department of Computer Science and Mathematics
Siirt University
Near East University
Department of Electrical and Electronics Engineering

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