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

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.