Mathematical modeling reveals spreading speed criteria in time-heterogeneous nonlocal diffusion systems, suggesting unified mechanisms for ecological invasion dynamics.
Key Points
To establish a unified framework based on generalized principal eigenvalues for determining spreading speeds in time-heterogeneous nonlocal diffusion equations.
Investigated properties, interrelationships, and sign criteria for three generalized principal eigenvalues in environments with a positive uniform mean value.
Constructed explicit upper and lower solutions on unbounded domains using test functions guided by eigenvalue signs.
Applied the framework to a Fisher-KPP equation with compact support and Holling I–III predator–prey systems under coinvasion and predator-invasion initial data.
Derived analytical sign criteria linking three generalized principal eigenvalue formulations in time-dependent nonlocal media.
Accurately characterized spreading speeds for compactly supported Fisher-KPP reaction-diffusion equations.
Determined spatiotemporal invasion speeds for predator–prey models across Holling-type I–III responses under both coinvasion and predator-only initial conditions.