Jing Xia, Zhixian Yu, Rong Yuan
Abstract:
This article concerns a symmetrical Lotka-Volterra predator-prey system
with delays. By analyzing the associated characteristic equation of
the original system at the positive equilibrium and choosing
the delay as the bifurcation parameter, the local stability and Hopf
bifurcation of the system are investigated. Using the normal form
theory, we also establish the direction and stability of the Hopf bifurcation.
Numerical simulations suggest an existence of Hopf bifurcation near
a critical value of time delay.
Submitted September 28, 2012. Published January 9, 2013.
Math Subject Classifications: 34K18, 37G05, 37G10, 92D25.
Key Words: Predator-prey system; delay; stability;
Hopf bifurcation; normal form.
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Jing Xia School of Mathematical Sciences Peking University, Beijing 100871, China email: xiajing2005@mail.bnu.edu.cn |
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Zhixian Yu College of Science University of Shanghai for Science and Technology Shanghai 200093, China email: yuzx0902@yahoo.com.cn |
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Rong Yuan School of Mathematical Sciences Beijing Normal University Beijing 100875, China email: ryuan@bnu.edu.cn |
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