Effect of the protection zone on coexistence of the species for a ratio-dependent predator-prey model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Zeng, Xianzhong¹  Zeng, Wantong¹  Liu, Lingyu¹ 

[1] Hunan Univ Sci & Technol, Sch Math & Comp Sci, Xiangtan 411201, Peoples R China

关键词: Ratio-dependent predator-prey model;    Protection zone;    Critical value;    Coexistence;   

DOI  :  10.1016/j.jmaa.2018.02.060

来源: Elsevier

【 摘 要 】

This paper deals with the effect of the protection zone Omega(0) on coexistence of the species for a ratio-dependent predator-prey model. We obtain a critical value lambda(N)(1)(b delta(x), Omega) which is less than the well-known critical value lambda(D)(1) (Omega(0)) obtained in the previous literatures. Furthermore, we show that if lambda > lambda(N)(1) (b delta(x), Omega), then the prey persists regardless of the growth rates of the predator; while if lambda <=lambda(N)(1)(b delta(x), Omega), then there exists a real number mu*, such that the prey is ultimately extinct when mu>mu*. As for lambda< lambda(N)(1)(b delta(x), Omega) and mu

【 授权许可】

Free