We discuss a clacks of predator-prey systems under a sparse effect, which possess a dense dependence of the predator species. We prove that this system hasjust one singular point in the first quadrant and it must be a...We discuss a clacks of predator-prey systems under a sparse effect, which possess a dense dependence of the predator species. We prove that this system hasjust one singular point in the first quadrant and it must be a focus (or node).When it is stable, there can .at least exist two limit cycles surrounding it. Alsoa non-existential condition of limit cycles is given. When it is unstable, theremust exist a unique limit cycle surf.ounding it. Thus, the qualitative analysis ofthe system obtained is complete.展开更多
文摘We discuss a clacks of predator-prey systems under a sparse effect, which possess a dense dependence of the predator species. We prove that this system hasjust one singular point in the first quadrant and it must be a focus (or node).When it is stable, there can .at least exist two limit cycles surrounding it. Alsoa non-existential condition of limit cycles is given. When it is unstable, theremust exist a unique limit cycle surf.ounding it. Thus, the qualitative analysis ofthe system obtained is complete.
