Nonconstant steady states and pattern formations of generalized 1D cross‐diffusion systems with prey‐taxis. Issue 3 (17th January 2023)

• Record Type: Journal Article
• Authors: Luo, Demou; Wang, Qiru; Chen, Li
• Is Part Of: Studies in applied mathematics. Volume 150:Issue 3(2023)
• Page Start: 899
• Page End: 958
• Publication Date: 2023-01-17
• Subjects: 1D cross‐diffusion systems with prey‐taxis -- general functional responses -- nonconstant steady states -- pattern formations; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12560
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: Cross‐diffusion effects and tactic interactions are the processes that preys move away from the highest density of predators preferentially, or vice versa. It is renowned that these effects have played significant roles in ecology and biology, which are also essential to the maintenance of diversity of species. To simulate the stability of systems and illustrate their spatial distributions, we consider positive nonconstant steady states of a generalized cross‐diffusion model with prey‐taxis and general functional responses in one dimension. By applying linear stability theory, we analyze the stability of the interior equilibrium and show that even in the case of negative cross‐diffusion rate, which appeared in many models, the corresponding cross‐diffusion model has opportunity to achieve its stability. Meanwhile, in addition to the cross‐diffusion effect, tactic interactions can also destabilize the homogeneity of predator–prey systems if the tactic interaction coefficient is negative. Otherwise, taxis effects can stabilize the homogeneity.