Global solvability and stability of cognitive consumer-resource model with nonlocal usage of memory

In this paper, we formulate a consumer-resource system incorporating dynamic cognitive mapping and nonlocal memory integration. The model represents resource perception using a spatial convolution kernel, capturing nonlocal interactions between consumers and their environment. We establish the global existence of classical solutions under periodic boundary conditions in two spatial dimensions and demonstrate the global stability of homogeneous steady states within specific parameter regimes. Additionally, numerical simulations are conducted to explore the influence of the perception radius R on system dynamics. Our results reveal that the perception radius plays a pivotal role in inducing phase transitions from uniform states to complex spatiotemporal patterns, underscoring the significance of cognitive sensing scales in ecological self-organization.