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The limit cycles of a class of ecosystems with sparse effects. (Chinese. English summary) Zbl 0917.92029

Summary: This paper is devoted to study the following ecosystem model with sparse effects: \[ dx/dt=x^2(a-cx^2) -bxy/(x+k),\quad dy/dt=y(-d+abx/(x+k)). \] By using qualitative theory of ordinary differential equations, we obtained the region of existence, uniqueness and nonexistence of limit cycles of the above system.

MSC:

92D40 Ecology
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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