Journal
CHINESE PHYSICS B
Volume 23, Issue 1, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1674-1056/23/1/010501
Keywords
logistic map; impulse; periodic solutions; bifurcation mechanism
Categories
Funding
- National Natural Science Foundation of China [11202180, 61273106, 11171290]
- Natural Science Foundation of Jiangsu Province, China [BK2010292, BK2010293]
- Natural Science Foundation of the Jiangsu Higher Education Institutions of China [10KJB510026]
- National Training Programs of Innovation and Entrepreneurship for Undergraduates, China [201210324009]
- Training Programs of Practice and Innovation for Jiangsu College Students, China [2012JSSPITP2378]
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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 Poincare 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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