中国物理B ›› 2015, Vol. 24 ›› Issue (11): 110501-110501.doi: 10.1088/1674-1056/24/11/110501
Stability of a delayed predator–prey model in a random environment
靳艳飞a, 谢文贤b
- a Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China;
b Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China
Stability of a delayed predator–prey model in a random environment
Jin Yan-Fei (靳艳飞)a, Xie Wen-Xian (谢文贤)b
- a Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China;
b Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China
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 Itô 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.
中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)
- 05.40.-a