Chaotic behavior analysis of a new incommensurate fractional-order Hopfield neural network system

Debbouche, Nadjette and Ouannas, Adel and Batiha, Iqbal M. and Grassi, Giuseppe and Kaabar, Mohammed K. A. and Jahanshahi, Hadi and Aly, Ayman A. and Aljuaid, Awad M. (2021) Chaotic behavior analysis of a new incommensurate fractional-order Hopfield neural network system. Complexity, 2021. ISSN 1076-2787, DOI

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This study intends to examine different dynamics of the chaotic incommensurate fractional-order Hopfield neural network model. The stability of the proposed incommensurate-order model is analyzed numerically by continuously varying the values of the fractional-order derivative and the values of the system parameters. It turned out that the formulated system using the Caputo differential operator exhibits many rich complex dynamics, including symmetry, bistability, and coexisting chaotic attractors. On the other hand, it has been detected that by adapting the corresponding controlled constants, such systems possess the so-called offset boosting of three variables. Besides, the resultant periodic and chaotic attractors can be scattered in several forms, including 1D line, 2D lattice, and 3D grid, and even in an arbitrary location of the phase space. Several numerical simulations are implemented, and the obtained findings are illustrated through constructing bifurcation diagrams, computing Lyapunov exponents, calculating Lyapunov dimensions, and sketching the phase portraits in 2D and 3D projections.

Item Type: Article
Funders: Taif University, Taif, Saudi Arabia[TURSP-2020/229]
Uncontrolled Keywords: Stability;Synchronization
Subjects: Q Science > QA Mathematics
Depositing User: Ms Zaharah Ramly
Date Deposited: 14 Oct 2022 05:44
Last Modified: 14 Oct 2022 05:44

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