Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Mathematical Physics Pub Date : 2023-11-25 DOI:10.1155/2023/8942147
Hang Zhang, Yujuan Jiao, Jinmiao Yang
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Abstract

In this paper, we are concerned with traveling wave solutions for two preys–one predator system with switching effect. First, we discuss that there is no traveling wave solution for this system by using linearization method. Second, applying super-sub solution method we establish the existence of semitraveling wave solutions with the minimal speed explicitly defined. Moreover, using the method of Lyapunov function and LaSalle’s invariance principle, under certain conditions, we obtain that the semitraveling wave solutions connect the only positive equilibrium point at infinity, are actually traveling wave solutions. Finally, the numerical experiments support the validity of our theoretical results.
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具有切换效应的反应-扩散捕食者-捕食者系统行波解的存在性与不存在性
本文研究了具有切换效应的两捕食者-一捕食者系统的行波解。首先,我们用线性化方法讨论了该系统不存在行波解。其次,应用超次解方法,建立了明确定义最小速度的半行波解的存在性。此外,利用Lyapunov函数的方法和LaSalle的不变性原理,在一定条件下,我们得到了在无穷远处连接唯一正平衡点的半行波解实际上是行波解。最后,通过数值实验验证了理论结果的有效性。
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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