Work

Pattern dynamics of a cross-diffusion predator–prey model with nonlinear harvesting term

Year: 2025

Type: article

Abstract: In this paper, we investigate a cross-diffusion predator–prey model incorporating a nonlinear harvesting term, with a particular focus on the role of cross-diffusion in shaping Turing patterns of positive equilibria. The diffusion instability of the positive equilibrium of the model with Neumann boundary conditions is discussed. In order to better understand the influence of cross-diffusion on pattern formation, the pattern formation process without cross-diffusion is first given, and then the cross-diffusion coefficient is selected as the main control parameter to observe its influence on the prey pattern formation. Through a series of numerical simulations, diverse Turing structures in the parameter space are obtained, including hole, strip, and spot patterns. Finally, leveraging computer-aided analysis, we simulate spiral patterns under four distinct initial conditions. Our results collectively demonstrate that cross-diffusion significantly enriches the pattern dynamics of the predator–prey system, offering valuable insights into the spatio-temporal complexity and dynamic properties of such ecosystems.

Source: Advances in Continuous and Discrete Models

DOI: 10.1186/s13662-025-03921-z

Authors: Xinze Lian, Huihui Wu, Meng Zhu, Weimin Xu

Institutions: Wenzhou University of Technology, Wenzhou University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: hybrid

Estimated APC paid: $1,890

Funder: Natural Science Foundation of Zhejiang Province