Traveling waves for n-species competitive system with nonlocal dispersals and delays

Traveling Wave Solutions in Nonlocal Dispersal Models With Nonlocal Delays

“…Therefore, we improve some known results on the existence and asymptotic behavior of traveling wave solutions of some models, at least for the system studied in [22]. Moreover, we also present the nonexistence of nontrivial traveling wave solutions in Section 5 and we obtain the minimal wave speed of models in Xia et al [22], Yu and Yuan [24,Model 1.3], which completes these known conclusion.…”

“…These ideas were earlier used in the study of partial functional differential systems by Lin and Ruan [12]. Moreover, to illustrate our results, we shall investigate the existence and nonexistence of traveling wave solutions if (1.4) admits the following nonlinearity (see Xia et al [22], Yu and Yuan [24])…”

Uniqueness of traveling front solutions for the Lotka-Volterra system in the weak competition case

“…Moreover, there exists a family of traveling planar waves for (2) on R n with different types of reaction terms in [18]. In addition, when delays or nonlocal diffusion are taken into consideration in kinds of competition systems, there are a large number of papers focusing on the existence of traveling wave solutions, such as [3,5,10,11,12,13,14,15,16,21,22,23,24]. When the free boundary is considered, one can refer to [20].…”

Existence of traveling wave solutions in m-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction

“…which correct the inappropriate statement in [13,22], and can simplify the verification of upper-lower solution for system (4.3). Furthermore, we denote constants t i3 such that…”

“…Motivated by the work [13][14][15]22], in this paper, we will consider the existence of traveling wave solutions for system (1.4) with the nonlinearities f i satisfying the (exponential) competitive quasimonotone condition. By using the cross-iteration scheme and upper-lower solution method, we consider the traveling-wave solution problem for system (1.4), and give the existence result of traveling wave solutions for a delayed lattice competitive Lotka-Volterra system.…”