Spreading Speeds and Linear Determinacy for Two Species Competition Systems with Nonlocal Dispersal in Periodic Habitats

Traveling waves and spreading speeds for time–space periodic monotone systems

“…For monotone semiflows of bistable type, Fang and Zhao [9] interpreted the bistability from a monotone dynamical system point of view to find a link between the monostable subsystems and bistable system itself, which is used to establish the existence of bistable wavefronts. We refer to [21,6,34,35] for nonlocal dispersal equations, and two survey papers [43,15] for more references. There are also quite a few investigations on time-periodic fronts of reaction-diffusion equations, see, e.g., [1,2,10,26,46,47,45] and references therein.…”

“…For a reaction-diffusion competition model with seasonal succession, Ma and Zhao [26] studied the existence of single spreading speed and its linear determinacy, and showed that the spreading speed coincides with the minimal wave speed of time-periodic traveling waves. More recently, Kong, Rawal and Shen [21] proposed a competition model with nonlocal dispersal in a time and space periodic habitats, and investigated the spreading speed and its linear determinacy. For traveling waves in a time-delayed reaction-diffusion competition model with nonlocal terms, we refer to Gourley and Ruan [13].…”

“…For traveling waves in a time-delayed reaction-diffusion competition model with nonlocal terms, we refer to Gourley and Ruan [13]. It is worthy to point out that our approach is quite different from those in [21,28,32].…”