The role of protection zone on species spreading governed by a reaction-diffusion model with strong Allee effect

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Du, Kai¹  Peng, Rui²  Sun, Ningkui³ 

[1] Fudan Univ, Shanghai Ctr Math Sci, 2005 Songhu Rd, Shanghai 200438, Peoples R China

[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[3] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Shandong, Peoples R China

关键词: Reaction-diffusion equation;    Strong Allee effect;    Protection zone;    Species spreading;    Long time behavior;   

DOI  :  10.1016/j.jde.2018.11.035

来源: Elsevier

【 摘 要 】

It is known that a species dies out in the long run for small initial data if its evolution obeys a reaction of bistable nonlinearity. Such a phenomenon, which is termed as the strong Allee effect, is well supported by numerous evidence from ecosystems, mainly due to the environmental pollution as well as unregulated harvesting and hunting. To save an endangered species, in this paper we introduce a protection zone that is governed by a Fisher-KPP nonlinearity, and examine the dynamics of a reaction-diffusion model with strong Allee effect and protection zone. We show the existence of two critical values 0 < L-* <= L*, and prove that a vanishing-transition-spreading trichotomy result holds when the length of protection zone is smaller than L-*; a transition-spreading dichotomy result holds when the length of protection zone is between L-* and L*; only spreading happens when the length of protection zone is larger than L*. This suggests that the protection zone works when its length is larger than the critical value L-*. Furthermore, we compare two types of protection zone with the same length: a connected one and a separate one, and our results reveal that the former is better for species spreading than the latter. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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