Traveling waves in a nonlocal dispersal SIR model with critical wave speed

Minimal wave speed in a dispersal predator–prey system with delays

“…That is, for the minimal wave speed, the corresponding traveling wave solutions may have different properties. Moreover, there are also some results on the minimal wave speed of nonmonotone coupled systems with time delay, which was proved by constructing upper and lower solutions, part of recent results can be found in Fu [38], Lin [39] and Yang and Li [40]. In mathematical biology, the spreading speed is also an important threshold [41].…”

Traveling waves in a nonlocal dispersal predator-prey model

“…holds from (37). That is, ψ k (ξ) ≤ 1 + 1 k for every ξ ∈ R and 1 ≤ k ∈ N. Thus, ψ ∞ (ξ) ≤ 1 for every ξ ∈ R. Due to ψ ∞ (0) = 1, then the function ψ ∞ get a global maximum at 0 and ψ ∞ (0) = 0.…”

“…However, owing to the fact that the effect of nonlocal dispersal and the non-monotonic of predator-prey systems themselves, the study of traveling waves is very limited ( [35,41]). We only refer to the readers [27,29,37,39,38] for some nonlocal dispersal epidemic models with predator-prey property.…”

“…Meanwhile, the Dunbar's method and the monotone dynamical theory are all invalid for system (3). However, inspired by some works in [9,27,37,38,39], we will get the existence of traveling waves through constructing a truncate problem combining the supper and lower solutions method with Schauder's fixed-point theorem when c > c * (c * is the minimal wave speed). It is noticed that it is very difficult to determine the final state about traveling waves for system (3).…”

Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence

“…where R J(x − η)u(η, t)dη := J * u denotes the normal convolution. For other related works, one can refer to [17,18].…”