Cognitive Consumer-Resource Spatiotemporal Dynamics with Nonlocal Perception

Abstract

Nonlocal perception is crucial to the mechanistic modeling of cognitive animal movement. We formulate a diffusive consumer-resource model with nonlocal perception on resource availability, where resource dynamics is explicitly modeled, to investigate the influence of nonlocal perception on stability and spatiotemporal patterns. For the finite domain, nonlocal perception described by two common types of resource detection function (spatial average or Green function) has no impact on the stability of the spatially homogeneous steady state. For the infinite domain, nonlocal perception described by the Laplacian or Gaussian detection function has no impact on stability either; however, the top-hat detection function can destabilize the spatially homogeneous steady state when the rate of perceptual movement is large and the detection scale belongs to an appropriate interval. Using the more realistic top-hat perception kernel, we investigate the influence of the detection scale, the perceptual movement rate and the resource’s carrying capacity on the spatiotemporal patterns and find the stripe spatial patterns, oscillatory patterns with different spatial profiles as well as spatiotemporal chaos.