【摘要】 研究了一类捕食-食饵模型,其中捕食者的密度干扰项的系数与食饵密度有关。首先,利用Leray-Schauder度理论,通过计算不动点的指数,结合特征值的比较原理得出了正平衡解存在的充分条件;然后,利用Turing理论,讨论了该模型半平凡解的稳定性情况;最后讨论了解的渐近行为,运用半动力系统的一致持续理论给出了正解一致持续的充分条件。更多还原

【Abstract】 The predator-prey model whose predator′s density interference term′s coefficient is related with prey is investigated.First,by calculating the index of the fixed point,some sufficient conditions for the existence of positive steady-state solutions are obtained.Furthermore,the stability of the semi-trivial solutions is discussed by Turing theory.Finally,the asymptotic behavior of solutions is discussed,and by applying permanence theory in semi-dynamical systems sufficient conditions for the permanence of this system are derived.更多还原