Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system

• Published in: Chaos, solitons and fractals solitons and fractals, 2023-04, Vol.169, p.113275, Article 113275
• Main Authors: Ren, Lei, Lin, Ming-Hung, Abdulwahab, Abdulkareem, Ma, Jun, Saberi-Nik, Hassan
• Format: Article
• Language: English
• Subjects: 4D hyperchaotic Rabinovich system; Hamilton energy; Lagrange multiplier method; The Mittag-Leffler GASs
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2023.113275

In this paper, the dynamical behavior of integer and fractional 4D hyperchaotic Rabinovich system is studied. We use the Lagrange coefficient method to solve an optimization problem analytically so that find an accurate ultimate bound set (UBS) for the 4D hyperchaotic Rabinovich system. Furthermore, bifurcation diagrams, Lyapunov exponents, global attractive sets (GASs), and positive invariant sets (PISs) of the fractional-order system are studied. Finally, using the Mittag-Leffler function and Lyapunov function method, the Mittag-Leffler GAS and Mittag-Leffler PIS of the proposed system are estimated. Our investigations indicate that there is a close relationship between changing the parameters and the dynamical behavior of the system, Hamilton energy consumption and changing the bound of the variables. The corresponding boundedness is numerically verified to show the effectiveness of the theoretical analysis. •The Mittag-Leffler global attractive sets for the fractional system are estimated.•New explicit ultimate bound is clarified for 4D hyperchaotic Rabinovich.•The Hamilton energy function is defined to discern the energy dependence on attractors.