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The 3‐D bifurcation and limit cycles in a food‐chain model
Author(s) -
Zhu Lemin,
Huang Xuncheng
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1025
Subject(s) - mathematics , center manifold , corollary , limit (mathematics) , bifurcation , hopf bifurcation , chain (unit) , mathematical analysis , food chain , limit cycle , manifold (fluid mechanics) , differential equation , pure mathematics , nonlinear system , mechanical engineering , paleontology , physics , quantum mechanics , astronomy , engineering , biology
In this paper, by using a corollary to the center manifold theorem, we show that the 3‐D food‐chain model studied by many authors undergoes a 3‐D Hopf bifurcation, and then we obtain the existence of limit cycles for the 3‐D differential system. The methods used here can be extended to many other 3‐D differential equation models. Copyright © 2008 John Wiley & Sons, Ltd.