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Chin. Phys. B, 2014, Vol. 23(1): 010501    DOI: 10.1088/1674-1056/23/1/010501
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Bifurcation analysis of the logistic map via two periodic impulsive forces

Jiang Hai-Bo, Li Tao, Zeng Xiao-Liang, Zhang Li-Ping
School of Mathematics, Yancheng Teachers University, Yancheng 224002, China
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.
Keywords:  logistic map      impulse      periodic solutions      bifurcation mechanism     
Received:  15 May 2013      Published:  12 November 2013
PACS:  05.45.Ac (Low-dimensional chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11202180, 61273106, and 11171290), the Natural Science Foundation of Jiangsu Province, China (Grant Nos. BK2010292 and BK2010293), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 10KJB510026), the National Training Programs of Innovation and Entrepreneurship for Undergraduates, China (Grant No. 201210324009), and the Training Programs of Practice and Innovation for Jiangsu College Students, China (Grant No. 2012JSSPITP2378).
Corresponding Authors:  Jiang Hai-Bo     E-mail:  yctcjhb@gmail.com

Cite this article: 

Jiang Hai-Bo, Li Tao, Zeng Xiao-Liang, Zhang Li-Ping Bifurcation analysis of the logistic map via two periodic impulsive forces 2014 Chin. Phys. B 23 010501

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