Robust synchronization of chaotic fractional-order systems with shifted Chebyshev spectral collocation method. (English) Zbl 1515.65258
Summary: In this work, synchronization of fractional dynamics of chaotic system is presented. The suggested dynamics is governed by a system of fractional differential equations, where the fractional derivative operator is modeled by the novel Caputo operator. The nature of fractional dynamical system is non-local which often rules out a closed-form solution. As a result, an efficient numerical method based on shifted Chebychev spectral collocation method is proposed. The error and convergence analysis of this scheme is also given. Numerical results are given for different values of fractional order and other parameters when applied to solve chaotic system, to address any points or queries that may occur naturally.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35K57 | Reaction-diffusion equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 93C10 | Nonlinear systems in control theory |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
Keywords:
Chebyshev spectral method; Caputo fractional derivative; chaotic model; numerical simulationsReferences:
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