Novel Control Law for the Fractional-order Chaotic Duffing Map
Adel Ouannas, Iqbal M. Batiha, Amina–Aicha Khennaoui, Amjed Zraiqat, Abeer A. Al-Nana
Abstract
The work reported in this paper concerns a study of chaos control of fractional-order maps, especially the two-dimensional fractional-order Duffing map, which is outlined here in the sense of the Caputo h-difference operator. For the purpose of stabilizing the dynamics of the established map, some simple linear control laws are proposed and verified numerically. The chaos control is accomplished by introducing a novel result which its proof relies on selecting a suitable Lyapunov function and proper linear control law. Several numerical simulations are performed to emphasize the influence of the established scheme.
Topics & Concepts
Duffing equationChaoticOperator (biology)Control theory (sociology)Work (physics)Simple (philosophy)Function (biology)MathematicsOrder (exchange)Lyapunov functionControl (management)Computer scienceApplied mathematicsLawNonlinear systemEngineeringArtificial intelligencePhysicsEconomicsBiochemistryEpistemologyTranscription factorPhilosophyChemistryFinanceGeneQuantum mechanicsPolitical scienceRepressorMechanical engineeringBiologyEvolutionary biologyFractional Differential Equations SolutionsChaos control and synchronizationAdvanced Differential Equations and Dynamical Systems