一类食饵采取鹰鸽对策的阶段结构捕食模型性态分析

A Stage-structured Predator-prey Model with Prey Using Hawk-dove Tactics

建立和研究了一类食饵采取鹰鸽对策的阶段结构捕食模型.当收益大于损失时,成年食饵种群全都采取鹰策略,证明了系统的一致持续生存性,利用Lyapunov函数证明了正平衡点的全局稳定性.当收益小于损失时,成年食饵种群采取鹰鸽混合策略,讨论了边界平衡点的存在性,并分析了fold分支.通过极限系统理论和杜拉克判据研究了边界平衡点的全局稳定性.

A stage-structured predator-prey model with prey using hawk-dove tactics was formulated and studied.When gain is greater than cost,all the mature prey population adopts hawk tactic.The uniform persistence of the system was proved and the global stability of positive equilibrium was studied by using Lyapunov function.When gain is smaller than cost,mature prey population adopts hawk-dove tactics.The existence of boundary equilibria was discussed and fold bifurcation was analyzed.Moreover,the global stability of boundary equilibrium was studied by the limit system theory and Dulac criterion.