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math.AP2025
Long-time behaviour and bifurcation analysis of a two-species aggregation-diffusion system on the torus
José A. Carrillo, Yurij Salmaniw
We investigate stationary states, including their existence and stability, in a class of nonlocal aggregation-diffusion equations with linear diffusion and symmetric nonlocal inter…
math.AP2025
Dynamics of a coupled nonlocal PDE-ODE system with spatial memory: well-posedness, stability, and bifurcation analysis
Yurij Salmaniw, Di Liu, Junping Shi +1
Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. In this…