Chaos Detection of the Chen System with Caputo–Hadamard Fractional Derivative
Chuntao Yin
Abstract
In this paper, we investigate the chaotic behaviors of the Chen system with Caputo–Hadamard derivative. First, we construct some practical numerical schemes for the Chen system with Caputo–Hadamard derivative. Then, by means of the variational equation, we estimate the bounds of the Lyapunov exponents for the considered system. Furthermore, we analyze the dynamical evolution of the Chen system with Caputo–Hadamard derivative based on the Lyapunov exponents, and we found that chaos does exist in the considered system. Some phase diagrams and Lyapunov exponent spectra are displayed to verify our analysis.
Topics & Concepts
Lyapunov exponentHadamard transformChenMathematicsChaoticFractional calculusApplied mathematicsDerivative (finance)Dynamical system (definition)Dynamical systems theoryMathematical analysisComputer sciencePhysicsQuantum mechanicsBiologyFinancial economicsPaleontologyArtificial intelligenceEconomicsFractional Differential Equations SolutionsAdvanced Differential Equations and Dynamical SystemsMathematical and Theoretical Epidemiology and Ecology Models