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Chaos in fractional ordered Liu system. (English) Zbl 1189.34081
Summary: Present paper deals with fractional version of a dynamical system introduced by C. Liu, L. Liu and T. Liu [A novel three-dimensional autonomous chaos system, Chaos Solitons Fractals 39, No. 4, 1950–1958 (2009)]. Numerical investigations on the dynamics of this system have been carried out. Properties of the system have been analyzed by means of Lyapunov exponents. Furthermore the minimum effective dimensions have been identified for chaos to exist in commensurate and incommensurate orders. It is noteworthy that the results obtained are consistent with the analytical conditions given in the literature.
34C28Complex behavior, chaotic systems (ODE)
26A33Fractional derivatives and integrals (real functions)
34A08Fractional differential equations
45J05Integro-ordinary differential equations
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