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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 and fractional differential inclusions
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
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