Bifurcation analysis of the logistic map via two periodic impulsive forces

doi:10.1088/1674-1056/23/1/010501

Chin. Phys. B ›› 2014, Vol. 23 ›› Issue (1): 10501-010501.doi: 10.1088/1674-1056/23/1/010501

Bifurcation analysis of the logistic map via two periodic impulsive forces

姜海波, 李涛, 曾小亮, 张丽萍

School of Mathematics, Yancheng Teachers University, Yancheng 224002, China

收稿日期:2013-05-15 修回日期:2013-06-07 出版日期:2013-11-12 发布日期:2013-11-12
基金资助:
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).

Bifurcation analysis of the logistic map via two periodic impulsive forces

Jiang Hai-Bo (姜海波), Li Tao (李涛), Zeng Xiao-Liang (曾小亮), Zhang Li-Ping (张丽萍)

School of Mathematics, Yancheng Teachers University, Yancheng 224002, China

Received:2013-05-15 Revised:2013-06-07 Online:2013-11-12 Published:2013-11-12
Contact: Jiang Hai-Bo E-mail:yctcjhb@gmail.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: logistic map, impulse, periodic solutions, bifurcation mechanism

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.

Key words: logistic map, impulse, periodic solutions, bifurcation mechanism

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.Pq (Numerical simulations of chaotic systems)

姜海波, 李涛, 曾小亮, 张丽萍. Bifurcation analysis of the logistic map via two periodic impulsive forces[J]. Chin. Phys. B, 2014, 23(1): 10501-010501.

Jiang Hai-Bo (姜海波), Li Tao (李涛), Zeng Xiao-Liang (曾小亮), Zhang Li-Ping (张丽萍). Bifurcation analysis of the logistic map via two periodic impulsive forces[J]. Chin. Phys. B, 2014, 23(1): 10501-010501.

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Bifurcation analysis of the logistic map via two periodic impulsive forces

Bifurcation analysis of the logistic map via two periodic impulsive forces

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