SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2608-2630, January 2020.
Persistence or extinction of moving animal species is a fundamental question in spatial ecology. This paper focuses on the impact of habitat shift driven by climate change on the persistence and propagation of a population with birth pulse. We first present a class of impulsive reaction-diffusion models with heterogeneous nonlinear reaction in high-dimensional space and study their threshold dynamics. We provide the persistence criterion of the system in bounded domains, and prove the existence, uniqueness, and global attraction of a positive steady state. Then we extend the results from bounded domains to the whole space. Our results indicate how the speed of the shifting habitat edge and impulsive reproduction (or harvesting) rate determine the persistence and extinction of the population. Numerical simulations are presented to illustrate the theoretical results.

中文翻译：

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气候变化驱动生境转移的PDE和离散时间混合动物运动模型的持久性和传播性

SIAM应用数学杂志，第80卷，第6期，第2608-2630页，2020年1月。
运动动物物种的持久性或灭绝是空间生态学中的一个基本问题。本文着重研究气候变化驱动的生境转变对具有出生脉冲的人口的持久性和繁殖的影响。我们首先提出一类具有高维空间中非均质非线性反应的脉冲反应扩散模型，并研究其阈值动力学。我们提供系统在有界域中的持久性准则，并证明正稳态的存在性，唯一性和全局吸引性。然后，我们将结果从有界域扩展到整个空间。我们的结果表明，生境边缘的变化速度和冲动繁殖（或收获）速率决定了种群的持久性和灭绝性。