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

Kulpash Iskakova, Mohammad Mahtab Alam, Shabir Ahmad, Sayed Saifullah, Ali Akgül and Gülnur Yılmaz

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 208, issue C, 219-245

Abstract: 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).

Keywords: Bifurcations; Chaos; Poincaré mapping; Lyapunov exponent; Newton polynomial (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:208:y:2023:i:c:p:219-245

DOI: 10.1016/j.matcom.2023.01.024

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