有毒物影响的阶段结构捕食模型的稳定性  

Stability of a Stage Structured Predator-Prey Model with Toxicants Effect

作　　者：雷鸣[1] 

机构地区：[1]北华大学数学与统计学院,吉林吉林132033

出　　处：《北华大学学报（自然科学版）》2015年第6期705-710,共6页Journal of Beihua University（Natural Science）

基　　金：吉林省教育厅科学技术研究项目(2015133)

摘　　要：建立了有毒物影响的阶段结构捕食模型.利用微分方程定性与稳定性理论,讨论了该模型解的非负性和平衡点的局部渐近稳定性,获得了正平衡点全局渐近稳定的充分性条件.揭示了当食饵种群增长率和捕食者种群增长率均足够大时,模型中两种群将持续生存.A stage structure predator-prey model with toxicants effect was established. Using differential equation qualitative and stability theory,the non-negativity of solution are discussed and equilibrium points of the model are locally asymptotically stable, the sufficient conditions are obtained for the global asymptotic stability of the positive equilibrium points of the model. The phenomenon is revealed that when the increasing rate of prey species and the increasing rate of predator species are all sufficiently large, two species of the model will permanently survive.

关 键 词：阶段结构捕食模型 有毒物影响 全局渐近稳定性 

分 类 号：O175.14[理学—数学]