Bifurcation analysis of the logistic map via two periodic impulsive forces |
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| Authors: | Jiang Hai-Bo Li Tao Zeng Xiao-Liang Zhang Li-Ping |
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| Affiliation: | School of Mathematics, Yancheng Teachers University, Yancheng 224002, China |
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| Abstract: | The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincaré map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. |
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| Keywords: | logistic map impulse periodic solutions bifurcation mechanism |
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