Abstract In this paper, we study the wave propagation in a two-dimensional lattice dynamical system with global interaction, which arises in the study of a single species population with two age classes and a fixed maturation period living in a two-dimensional spatial unbounded environment. We consider the monostable case and show that for any given admissible speed, all the wave profiles propagating toward a fixed direction have the same asymptotic behaviors when they approach the limiting states, and they are unique up to translation. Moreover, we prove that all the wave profiles remain strictly increasing in the propagation process.

中文翻译：

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具有全局相互作用的二维晶格动力系统中的波传播

摘要 在本文中，我们研究了波在具有全局相互作用的二维晶格动力学系统中的传播，该系统是在研究生活在二维空间无界环境中具有两个年龄等级和固定成熟期的单一物种种群时出现的。 . 我们考虑单稳态情况，并表明对于任何给定的容许速度，所有向固定方向传播的波形在接近极限状态时都具有相同的渐近行为，并且它们在平移之前是唯一的。此外，我们证明了所有的波形在传播过程中保持严格增加。