Numerical Solutions and Synchronization of a Variable-Order Fractional Chaotic System

Abstract

In the present paper, we implement a novel numerical method for solving differential equations with fractional variableorder 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.