¹Institute of Systems Engineering, College of Water Resources and Hydroelectric Engineering, Wuhan University, Wuhan, China
²Henan Institute of science and technology, Xinxiang, China
³College of Water Resources and Hydroelectric Engineering, Wuhan University, Wuhan, China

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Abstract—Chaos may be degenerated because of the finite precision effect, hence, in this work, for given a new fractional order three-dimensional chaotic attractors, numerical investigations on the dynamics of this system have been carried out. The stability of equilibrium for the system is analyzed according to the qualitative theory. Furthermore, a new chaotic control technique is designed, the special compound structure of the new fractional order chaotic attractor is investigated, and some numerical simulations are proposed. The results show that the new fractional order chaotic system can generate complex compound structure under the control of the constant control parameter. This evolving procedure reveals the forming mechanisms of compound nature and finds some law which is very meaningful in investigating some complex chaotic dynamical phenomena.

Index Terms—Fractional order, chaotic system, compound structure.

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Cite: Xinjie Li, Wenxian Xiao, Zhen Liu, Wenlong Wan, Tiesong Hu, "A New Fractional Order Chaotic System and Its Compound Structure," Journal of Software vol. 8, no. 1, pp. 126-133, 2013.