Global Asymptotic Stability and Hopf Bifurcation in a Homogeneous Diffusive Predator-Prey System with Holling Type II Functional Response — Oak Academic Publishing
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Global Asymptotic Stability and Hopf Bifurcation in a Homogeneous Diffusive Predator-Prey System with Holling Type II Functional Response
College of Mathematics and Physics, Wenzhou University, Wenzhou, China
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Key Laboratory for Subtropical Oceans & Lakes Environment and Biological Resources Utilization Technology of Zhejiang, Wenzhou University, Wenzhou, China
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School of Life and Environmental Science, Wenzhou University, Wenzhou, China
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School of Life and Environmental Science, Wenzhou University, Wenzhou, China
1 College of Mathematics and Physics, Wenzhou University, Wenzhou, China
2 Key Laboratory for Subtropical Oceans & Lakes Environment and Biological Resources Utilization Technology of Zhejiang, Wenzhou University, Wenzhou, China
3 School of Life and Environmental Science, Wenzhou University, Wenzhou, China
4 School of Life and Environmental Science, Wenzhou University, Wenzhou, China
In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠ 0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.
KeywordsHolling Type II Functional ResponseReaction-Diffusion Predator-Prey SystemGlobal StabilityTuring InstabilityHopf Bifurcation
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