一类捕食者染病的捕食者-食饵系统的随机动力学行为  

Stochastic Dynamics of a Predator-prey System with Disease in Predator

作　　者：冯涛[1] 孟新柱[1] FENG Tao MENG Xinzhu(College of Mathematics and Systems Science,Shandong University of Science and Technology, Qingdao, Shandong 266590,Chin)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《山东科技大学学报（自然科学版）》2017年第1期99-110,共12页Journal of Shandong University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(11371230;11501331);山东省自然科学基金项目(ZR2015AQ001;BS2015SF002);山东科技大学科研创新团队项目(2014TDJH102)

摘　　要：考虑了一类具有Beddington-DeAngelis功能性反应和Lévy跳的捕食者染病的捕食者-食饵系统的动力学行为。利用Lyapunov方法和伊藤公式,本文讨论了系统全局正解的存在唯一性;研究了随机系统在其确定性模型的平衡点周围的长时间行为。研究结果表明,在一定条件下,随机系统的解会在其确定性系统的平衡点周围波动,且波动的幅度与随机系统所受干扰的强度呈正相关。最后,本文运用Matlab数值模拟对前述理论进行了验证。This paper investigated the stochastic dynamics of an infected predator-prey model with Beddington-DeAngelis functional response and Lévy jump.By using Lyapunov methods and It＇s formula,this paper first discussed the existence and uniqueness of the global positive solution of the stochastic system,and then studied the asymptotic behaviors around the equilibrium points of its deterministic model.Results show that the solutions of the stochastic system fluctuate around the equilibrium points of its deterministic model under certain conditions,and the fluctuation intensity is positively correlated with the intensity of interference.Finally,numerical simulations were carried out to verify the theoretical findings.

关 键 词：捕食者-食饵系统 BEDDINGTON-DEANGELIS功能性反应 渐近行为 随机扰动 Lévy跳 

分 类 号：O175[理学—数学]