摘要
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influ- ences 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 Poincar6 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.
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influ- ences 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 Poincar6 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.
基金
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)
the Training Programs of Practice and Innovation for Jiangsu College Students,China(Grant No.2012JSSPITP2378)
