Periodic solutions and flip bifurcation in a linear impulsive system |
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Authors: | Jiang Gui-Rong and Yang Qi-Gui |
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Institution: | 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 |
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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. |
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Keywords: | linear impulsive equation periodic solution flip bifurcation |
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