Applied Mathematics and Mechanics

, Volume 21, Issue 7, pp 767–774 | Cite as

Hopf bifurcation for a ecological mathematical model on microbe populations

  • Guo Ruihai
  • Yuan Xiaofeng


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 words

mathematical model qualitative theory equilibrium points Hopf bifurcation 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Guo Ruihai
    • 1
  • Yuan Xiaofeng
    • 2
  1. 1.Department of MathematicsSouthwest Nationalities CollegeChengduP R China
  2. 2.Center for Mathematical SciencesCICA, Academia SinicaChengduP R China

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