Propagation dynamics for lattice differential equations in a time-periodic shifting habitat

Spatial propagation of a lattice predation–competition system with one predator and two preys in shifting habitats

“…Note that, by (19), there exist 𝑧 1 > 0 and 𝑧 2 > 0 such that ) defined by ( 18) are a pair of generalized super-and subsolutions of (4).…”

“…Hu and Li 15 first studied the persistence and spreading speed for the lattice Kolmogorov-Petrovski-Piskuno (KPP) equation in a shifting environment. Pan and Wu 19 further established the existence, uniqueness, and attractiveness of the periodic forced waves for the lattice differential equations in a time-periodic shifting habitat. For the lattice competition systems, Meng et al 18 distinguished the long-time behaviors in the case of weak competition and Wang et al 20 established the forced waves and gap formations when the resource functions of two competing species have different monotony properties, while Zhu et al 33 obtained the existence of multitype forced waves for both cases of weak competition and strong-weak competition when the two resource functions have same monotony properties.…”

Recent developments on spatial propagation for diffusion equations in shifting environments

“…On the other hand, we can find from the proof of [95, Theorem 2.1] that under (H 0 ), the considered model admits a forced wave connecting 0 to r(∞) with any forced speed c > −c * LDE (∞). Very recently, Pan and Wu [77] derived some spreading properties as well as the existence of time periodic forced wave for the lattice differential equations in a time-periodic shifting habitat as (H 3 ). These results are similar to that of continuously spatial model described by random diffusion and nonlocal dispersal equations.…”