Structural sensitivity of spatiotemporal pattern formation

The formation of spatiotemporal patterns in reaction-diffusion-type models of interacting populations is a fascinating area of research, offering insights into the stationary and dynamic coexistence of species within natural habitats. Mathematical models, both proposed and well-established, can exhibit a wide range of patterns depending on the nature of intra- and inter-species interactions. It is often assumed that a model's properties are robust to specific parameterizations of functional responses, which act as the links between trophic levels. A natural question arises: Do the bifurcation structures of the system remain stable as long as different functions are qualitatively similar? However, recent findings indicate the structural sensitivity of bifurcation scenarios for functionally equivalent response functions in temporal models. The primary objective of this talk is to extend such discussions on structural sensitivity to spatially explicit models of population dynamics. The discussion will focus on a system of two nonlinear reaction-diffusion-advection equations, where the functional response is parameterized by three distinct yet numerically similar functions.