疾病影响下一类具有阶段结构和比率依赖的随机捕食−食饵模型的动力学分析  

Dynamics analysis of a stochastic predator-prey model with stage structure and ratio-dependent in the effect of disease

作　　者：刘萍[1] 韩秋珂 谢婷 LIU Ping;HAN Qiuke;XIE Ting(School of Mathematics and Statistics,Yunnan University,Kunming 650500,Yunnan,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650500

出　　处：《云南大学学报（自然科学版）》2024年第6期1009-1020,共12页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11961078).

摘　　要：研究了一类疾病影响下具有阶段结构和比率依赖的随机捕食−食饵模型.首先,证明模型在任意初值条件下存在唯一的全局正解;其次,通过构造合适的Lyapunov函数,证明模型在一定的参数限制下存在遍历平稳分布;然后,运用伊藤公式和微分不等式放缩等,获得了种群灭绝的充分条件;最后,利用数值模拟验证了理论结果的可行性.We deal with a stochastic predator-prey model with stage structure and ratio-dependent in the effect of disease.Firstly,a unique global positive solution for the model with any positive initial value is proved.Then,by constructing an appropriate Lyapunov function,we investigate that the model has an ergodic stationary distribution under certain parametric restrictions.Further,sufficient conditions for populations extinction are obtained by using Itôformula and differential inequality scaling.Finally,numerical simulations have been carried out to validate the feasibility of our theoretical results.

关 键 词：随机捕食−食饵模型 阶段结构 比率依赖 疾病 平稳分布 

分 类 号：O175.14[理学—数学]