Work

Well‐Posedness and Pattern Formation in a Two‐Species Reaction–Diffusion System with Nonlocal Perception

Year: 2026

Type: article

Abstract: ABSTRACT Nonlocal perceptual cues, such as visual, auditory, and olfactory signals, profoundly influence animal movement and the emergence of ecological patterns. To capture these effects, we introduce a two‐species reaction–diffusion system with mutual nonlocal perception on a two‐dimensional periodic domain. We establish global well‐posedness of the model through a generalized entropy framework that accommodates nonlinear reaction kinetics and convolution‐based perception fields. Specializing to a predator–prey interaction, we carry out linear stability and bifurcation analyses with perceptual diffusion coefficients as bifurcation parameters. Explicit criteria are derived for the onset of Turing and Turing–Hopf instabilities, showing how perception radius and behavioral response jointly drive spatial self‐organization. Numerical simulations with a Holling Type II response illustrate both stationary and oscillatory heterogeneous patterns. Our results reveal complementary mechanisms linking perceptual range and movement tendencies within and across species, offering new theoretical insight into the role of nonlocal perception in ecological pattern formation.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.70186

Authors: Yaqi Chen, Ben Niu, Hao Wang

Institutions: Harbin Institute of Technology, University of Alberta

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: $4,550

Funders: Canada Research Chairs, China Scholarship Council, Natural Science Foundation of Shandong Province, Natural Sciences and Engineering Research Council of Canada