中国物理B ›› 2008, Vol. 17 ›› Issue (11): 4114-4122.doi: 10.1088/1674-1056/17/11/026

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Periodic solutions and flip bifurcation in a linear impulsive system

蒋贵荣, 杨启贵   

  1. School of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China;School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
  • 收稿日期:2008-05-20 修回日期:2008-06-09 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10572011, 100461002, and 10661005) and the Natural Science Foundation of Guangxi Province, China (Grant Nos 0575092 and 0832244).

Periodic solutions and flip bifurcation in a linear impulsive system

Jiang Gui-Rong (蒋贵荣)ab, Yang Qi-Gui (杨启贵)a   

  1. a School of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China; b School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
  • Received:2008-05-20 Revised:2008-06-09 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10572011, 100461002, and 10661005) and the Natural Science Foundation of Guangxi Province, China (Grant Nos 0575092 and 0832244).

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摘要： In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.

关键词: linear impulsive equation, periodic solution, flip bifurcation

Abstract: In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.

Key words: linear impulsive equation, periodic solution, flip bifurcation

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq