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bifurcationsandchaosinadiscretepredatorpreysystemwithhollingtypeivfunctionalresponse
Jicai Huang
2005
Source Publicationactamathematicaeapplicataesinica
ISSN0168-9673
Volume021Issue:001Pages:157
AbstractA discrete predator-prey system with Holling type-IV functional response obtained by the Euler method is first investigated. The conditions of existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory. Furthermore, we give the condition for the occurrence of codimension-two bifurcation called the Bogdanov-Takens bifurcation for fixed points and present approximate expressions for saddle-node, Hopfand homoclinic bifurcation sets near the Bogdanov-Takens bifurcation point. We also show the existence of degenerated fixed point with codimension three at least. The numerical simulations, including bifurcation diagrams, phase portraits, and computation of maximum Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors such as the attracting invariant circle, period-doubling bifurcation from period-2,3,4 orbits.interior crisis, intermittency mechanic, and sudden disappearance of chaotic dynamic.
Language英语
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/37298
Collection中国科学院数学与系统科学研究院
Affiliation中国科学院数学与系统科学研究院
Recommended Citation
GB/T 7714
Jicai Huang. bifurcationsandchaosinadiscretepredatorpreysystemwithhollingtypeivfunctionalresponse[J]. actamathematicaeapplicataesinica,2005,021(001):157.
APA Jicai Huang.(2005).bifurcationsandchaosinadiscretepredatorpreysystemwithhollingtypeivfunctionalresponse.actamathematicaeapplicataesinica,021(001),157.
MLA Jicai Huang."bifurcationsandchaosinadiscretepredatorpreysystemwithhollingtypeivfunctionalresponse".actamathematicaeapplicataesinica 021.001(2005):157.
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