Yang, Pinghua; Xu, Rui; Zhang, Shijun The limit cycles of a class of ecosystems with sparse effects. (Chinese. English summary) Zbl 0917.92029 J. Biomath. 12, No. 4, 335-338 (1997). 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 Keywords:equilibrium point; existence; uniqueness; limit cycles PDFBibTeX XMLCite \textit{P. Yang} et al., J. Biomath. 12, No. 4, 335--338 (1997; Zbl 0917.92029)