Fractional ordered Liu system with time-delay. (English) Zbl 1222.34005
Summary: The effect of delay on the chaotic behaviour has been investigated for the first time in the literature. In this regard fractional ordered Liu system [X.-Y. Wang and M.-J. Wang, Chaos 17, No. 3, 033106, 6 p. (2007; Zbl 1163.37382)] has been chosen as an example. Numerical simulations for various fractional orders corresponding to different values of delay have been carried out. It has been demonstrated that the chaotic systems can be transformed into limit cycles or stable orbits with appropriate choice of delay parameter.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 45J05 | Integro-ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Keywords:
Caputo derivative; fractional order dynamical systems; attractor; delay differential equations; predictor; corrector methodCitations:
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