羊群行为
图灵
捕食
统计物理学
霍普夫分叉
理论(学习稳定性)
人口
应用数学
分叉
数学
计算机科学
物理
生态学
非线性系统
生物
放牧
人口学
机器学习
林业
地理
量子力学
社会学
程序设计语言
作者
Fethi Souna,Salih Djilali,Abdelkader Lakmeche
标识
DOI:10.1140/epjp/s13360-021-01489-7
摘要
In this manuscript, we investigate the fear effect on the spatiotemporal behavior of the predator–prey model with prey social behavior and cross-diffusive. Our main interest is to determine the existence of Turing patterns and the fear effect performed by predators on the prey population and the group defense. The fear can lead to a partition of the prey herd which is known as prey escaping. It is obtained that the system has rich dynamics elaborated by the presence of Turing patterns and Turing–Hopf bifurcation. The nature of Turing patterns is successfully discussed by analyzing the amplitude equations with a multiple-timescale technique. After studying the stability of these amplitude equations, it has been identified various Turing patterns driven by the cross-diffusion. Further, the effect of the fear rate or escaping rate on the behavior of the solution is discussed. The theoretical results are checked numerically.
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