Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays

N. Ramesh Babu and P. Balasubramaniam

Chaos, Solitons & Fractals, 2022, vol. 162, issue C

Abstract: In this paper, a new fractional differentiation operator is considered the convolution of a power law with a fractal derivative. The novel operator sought to attract more non-local memory effects and self-similarities in chaotic attractors. This paper addresses the problem of fractal-fractional order quaternion-valued neural networks (FFoQVNNs) with time-varying delays. The sufficient conditions for the existence and uniqueness of an equilibrium point are derived for the proposed model by employing contraction mapping. The Lyapunov direct technique and fractal-fractional differential theory achieve the finite-time synchronization criteria by dividing the FFoQVNNs into four real-valued systems. Furthermore, the settling time is determined, which impact by the fractal dimension β, fractional-order α, and control parameters. Finally, a corresponding numerical simulation is demonstrated to show the accuracy of the theoretical results.

Keywords: Fractal-fractional derivative; Finite-time synchronization; Chaotic attractors; Lyapunov functional; Quaternion-valued neural networks (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006889

DOI: 10.1016/j.chaos.2022.112478

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