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.


34C28 Complex behavior and chaotic systems of ordinary differential equations
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
45J05 Integro-ordinary differential equations
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