Hopf bifurcation for a ecological mathematical model on microbe populations
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The ecological model of a class of the two microbe populations with second-order growth rate was studied. The methods of qualitative theory of ordinary differential equations were used used in the four-dimension phase space. The qualitative property and stability of equilibrium points were analysed. The conditions under which the positive equilibrium point exists and becomes and O+ attractor are obtained. The problems on Hopf bifurcation are discussed in detail when small perturbation occurs.
Key wordsmathematical model qualitative theory equilibrium points Hopf bifurcation
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- [ 1 ]
- [ 2 ]Nemenskii B. B, Sichepalov B. B.Qualitative Theory of Differential Equation [M]I. Wang Rouhai transl. Beijing: Science Press, 1959,201 ∼ 230. (Chinese version)Google Scholar
- [ 3 ]Liu Shize. Topologicl classification of singular points inn-dimensional space [J].Mathematical Advance, 1965,8(3):217 ∼ 242. (in Chinese)Google Scholar
- [ 4 ]Hartman P.Ordinary Differential Equation[M]. Boston: Birkhauser,1982,228 ∼ 250.Google Scholar
- [ 5 ]Li Jibin, Feng Beiye.Stability, Bifurcations and Chaos [M]. Kunmin: Yunnan Science and Technology Publishing House, 1995,85 ∼ 127. (in Chinese)Google Scholar
- [ 6 ]Wiggins S.Introduction to Applied Nonlinear Dynamical System and Chaos [M]. New York: Springer-Verlag,1990,193 ∼ 284.Google Scholar
- [ 7 ]