【摘要】 本文在假定成年个体会对幼年个体进行同类捕食和考虑幼年个体自然死亡的基础上,建立了一类具有两阶段结构的同类相食模型.当种群不存在同类捕食时,通过构造Lyapunov函数分别得到了种群灭绝平衡点和种群存活平衡点的全局渐近稳定的条件.对于种群存在同类捕食的情形,发现模型会同时存在两个种群存活平衡点和发生鞍结点分支,并通过构造Dulac函数排除周期解的存在性,得到模型的全局动力学性态.种群存活的两个平衡点的存在和鞍结点分支的发生意味着种群发展的最终状态会依赖于模型的初始条件.所得理论结果均得到了数值模拟的验证.更多还原

【Abstract】 Based on the assumptions that the adult could kill and eat the juvenile of the same species and that there is the natural death of the juvenile, a two-stage-structured model with cannibalism is proposed in this paper. In the absence of cannibalism, the conditions ensuring the global stabilities of the population extinction and survival equilibria of the model are obtained by constructing the corresponding Lyapunov functions. In the presence of cannibalism, it is found that the model may have two population survival equilibria and that the saddle-node bifurcation can occur for certain parameter region, and the global dynamics is determined by constructing the Dulac function to rule out the existence of periodic solutions. The existence of two positive equilibria and the occurrence of the saddle-node bifurcation imply that the final state of the population growth depends on the initial condition of the model. The theoretic results obtained are verified by numerical simulation.更多还原