ABSTRACT This paper examines a three‐species food‐chain model with spatially heterogeneous resource distributions, in which only the intermediate consumers undergo diffusion. Our analysis reveals the following key insights: (i) When the mortality rate of intermediate consumers increases beyond a critical threshold, the intermediate consumers undergo eventual extinction, and top predators will also face ultimate elimination, provided that their mortality rate exceeds a corresponding critical value; (ii) a unique positive steady state emerges when both and are maintained at sufficiently low levels. Notably, in contrast to conventional studies indicating that predators cannot survive without prey, our results demonstrate that the diffusive movement of intermediate consumers enables their survival and invasion into spatial domains lack of basal resources. This finding highlights the intricate interplay between diffusion processes and spatially heterogeneous resource distributions in shaping the dynamic behaviors of food‐chain models.
Ge et al. (Fri,) studied this question.