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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.
34A08Fractional differential equations
34D20Stability of ODE
37D45Strange attractors, chaotic dynamics
45J05Integro-ordinary differential equations
26A33Fractional derivatives and integrals (real functions)
65L06Multistep, Runge-Kutta, and extrapolation methods