CHAOTIC BEHAVIOR IN DISCRETE CHEN SYSTEM WITH FRACTIONAL ORDER
A. George Maria Selvam
Department of Mathematics, Sacred Heart College, Tirupattur – 635 601, Vellore Dt., Tamil Nadu, S.India. , IN
M. Paul Loganathan
Department of Mathematics, Sacred Heart College, Tirupattur – 635 601, Vellore Dt., Tamil Nadu, S.India. , IN
R. Janagaraj
Department of Mathematics, Sacred Heart College, Tirupattur – 635 601, Vellore Dt., Tamil Nadu, S.India. , IN
D. Abraham Vianny
Department of Mathematics, Sacred Heart College, Tirupattur – 635 601, Vellore Dt., Tamil Nadu, S.India. , IN
Keywords: Fractional Order Differential Equations, Chen System, Discrete Time, Fixed Points, Stability, Chaotic Attractor.
Abstract
Guanrong Chen and Ueta found a simple three dimensional autonomous system in 1999 and this system is not topologically similar to Lorenz’s system as well as a double scroll chaotic attractor. This work examins the dynamical nature of the fractional discrete time Chen system with order between zero and one. The ordinary differential equation of the Chen system is described by the following form Here abc , , assume non-zero positive values. Applying a discretization process, its discrete version of FO Chen system is obtained. Fixed points are obtained and using Routh-Hurwitz criteria, the stability of the system is analysed. Numerical verification are presented for the analysis of dynamical properties of the system. Time series and phase orbit diagrams for the discrete time FO Chen system are constructed. Numerically solving the system of discrete fractional order 3-D Chen system, chaotic nature is explained. For the discrete time FO system, chaotic attractor exists for different parameter values. 2010 Mathematics Subject Classification. – 26A33, 39A12, 37C25, 37C75
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