Stability of a delayed predator prey model in a random environment  

作　　者：靳艳飞 谢文贤 

机构地区：[1]Department of Mechanics, Beijing Institute of Technology [2]Department of Applied Mathematics, Northwestern Polytechnical University

出　　处：《Chinese Physics B》2015年第11期140-145,共6页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11272051 and 11302172)

摘　　要：The stability of the first-order and second-order solution moments for a Harrison-type predator-prey model with parametric Gaussian white noise is analyzed in this paper. The moment equations of the system solution are obtained under Ito interpretations. The delay-independent stable condition of the first-order moment is identical to that of the deterministic delayed system, and the delay-independent stable condition of the second-order moment depends on the noise intensities. The corresponding critical time delays are determined once the stabilities of moments lose. Further, when the time delays are greater than the critical time delays, the system solution becomes unstable with the increase of noise intensities. Finally, some numerical simulations are given to verify the theoretical results.The stability of the first-order and second-order solution moments for a Harrison-type predator-prey model with parametric Gaussian white noise is analyzed in this paper. The moment equations of the system solution are obtained under Ito interpretations. The delay-independent stable condition of the first-order moment is identical to that of the deterministic delayed system, and the delay-independent stable condition of the second-order moment depends on the noise intensities. The corresponding critical time delays are determined once the stabilities of moments lose. Further, when the time delays are greater than the critical time delays, the system solution becomes unstable with the increase of noise intensities. Finally, some numerical simulations are given to verify the theoretical results.

关 键 词：delay-independent stability predator-prey model moment equations environmental noise 

分 类 号：O175[理学—数学]