In the present paper, we study the long-time behavior of a class of diffusive predator–prey systems with fear cost and protection zone. The sufficient conditions for the extinction and persistence are established by using upper–lower solution method and comparison principle. The analytical results suggest that fear cost and protection zone have a significant impact on the dynamics.

中文翻译：

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一类具有恐惧成本和保护区的扩散捕食－被捕食系统的长期行为

在本文中，我们研究了一类具有恐惧成本和保护区的扩散捕食－被捕食系统的长期行为。利用上下解法和比较原理，建立了灭绝和持久性的充分条件。分析结果表明，恐惧成本和保护区对动力学有重大影响。