Numerical solutions and synchronization of a variable-order fractional chaotic system

Year 2021, Volume: 1 Issue: 1, 11 - 23, 30.09.2021

Zakia Hammouch Mehmet Yavuz Necati Özdemir

https://doi.org/10.53391/mmnsa.2021.01.002

Cited By: 58

Abstract

In the present paper, we implement a novel numerical method for solving differential equations with fractional variable-order in the Caputo sense to research the dynamics of a circulant Halvorsen system. Control laws are derived analytically to make synchronization of two identical commensurate Halvorsen systems with fractional variable-order time derivatives. The chaotic dynamics of the Halvorsen system with variable-order fractional derivatives are investigated and the identical synchronization between two systems is achieved. Moreover, graph simulations are provided to validate the theoretical analysis.

Keywords

Variable-order fractional derivative, chaotic system, Lyapunov exponent, synchronization

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