阿利效应
图案形成
霍普夫分叉
图灵
数学
不稳定性
常量(计算机编程)
扩散
统计物理学
分叉
理论(学习稳定性)
数学分析
物理
生物
计算机科学
非线性系统
量子力学
人口
人口学
社会学
遗传学
机器学习
程序设计语言
标识
DOI:10.1016/j.chaos.2023.113456
摘要
In this paper, a diffusive predator–prey model with Allee effect and functional response of generalized Holling type IV is established. The complex pattern dynamics of and bifurcation phenomena of system are analyzed by using linear stability analyses and bifurcation theory, etc. Corresponding to spiral pattern, spot pattern or spot–stripe mix pattern and chaotic pattern, respectively, the conditions that arise Hopf instability, Turing instability and Hopf–Turing instability of constant positive steady solutions of reaction–diffusion system are presented. The impacts of Allee effect and cross-diffusion on pattern formations of the system are further discussed. Particularly, provided that cross-diffusion is absent, there will not appear the formation of Turing pattern, that is, Turing pattern is only driven by cross-diffusions. Addressed to the different pattern formations involving in cross-diffusion and Allee effect, overall numerical simulations are provided when the spatial dimension is two and the theoretical results are demonstrated. It is revealed that the larger Allee effect constant A and the cross-diffusion coefficient d4 are advantageous for the appearing of formation of Turing pattern, while the cross-diffusion coefficient d3 suppresses the formation of Turing pattern with its increasing.
科研通智能强力驱动
Strongly Powered by AbleSci AI