Numerical Solutions and Synchronization of a Variable-Order Fractional Chaotic System
Zakia Hammouch, Mehmet Yavuz, Necati Özdemir
2021Mathematical Modelling and Numerical Simulation with Applications124 citationsDOIOpen Access PDF
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.
Topics & Concepts
Synchronization (alternating current)Order (exchange)Variable (mathematics)Chaotic systemsChaoticMathematicsApplied mathematicsControl theory (sociology)Computer scienceMathematical analysisTopology (electrical circuits)EconomicsCombinatoricsFinanceArtificial intelligenceControl (management)Chaos control and synchronizationNeural Networks and ApplicationsFractional Differential Equations Solutions