Abstract Spatial memory is inevitable in animal movement modeling but elusive in many classical models. A nonlocal integral term involving space is a traditional way to incorporate spatial memory, but the actual spatial memory should depend on past information so that delay naturally arises. We propose a new consumer‐resource model with random and memory‐based diffusions in which the resource species has no memory or cognition, whereas the consumer species has spatial memory. By using the memory‐based diffusion coefficient and the averaged memory period of the consumer as the control parameters, we find Hopf bifurcations and stability switches occur and spatially nonhomogeneous periodic solutions are generated. It is well known that prey‐taxis enhances the stability of a homogeneous coexistence state in a predator–prey system, and here we show that memory‐based prey‐taxis can destabilize a constant coexistence and generate complex spatiotemporal pattern formation. Using the obtained theoretical results, we study the impact of the memory‐based diffusion on the consumer‐resource dynamics with Holling type‐I and type‐II functional responses.
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