Traveling wave phenomena of a nonlocal reaction-diffusion equation with degenerate nonlinearity

Traveling wave solutions for three-species nonlocal competitive-cooperative systems

“…To make the model more practical in applications, nonlocal effects and timedelays have been considered [3,6,7,10,23]. Subsequently, the traveling wave solution of this model has been studied and developed, see [11,18,19,25,29].…”

Turing Patterns for a Nonlocal Lotka–Volterra Cooperative System

“…Therefore, it is of great significance to understand the cause and mechanism of pattern formation for revealing the mystery of nature formation. In order to understand its formation mechanism, many scholars turned their work to study various mathematical models with different factors, such as delay [14,16,36], noise [19], network [25,28,34], season [29] and so on, among which, the reactiondiffusion equation was often used in [1,22] and the references therein.…”

“…Then, Yan and Guo [31] further extended the above conclusion to Lotka-Volterra model with cross-diffusion and delay effect. And Han and Wang [14] also studied the following Lotka-Volterra competition diffusion system with nonlocal term where * * u and * * v are similar to model (1.1) with (1.2). Through using the multi-scale analysis and numerical simulation, they obtained the pattern of system (1.4) under what conditions and gave the verification.…”