Abstract In this paper we study speed selection for traveling wavefronts of the lattice Lotka-Volterra competition model. For the linear speed selection, by constructing new types of upper solutions to the system, we widely extend the results in the literature. We prove that, for the nonlinear speed selection, the wavefront of the first species decays with a faster rate at the far end. This enables us to construct novel lower solutions to establish the existence of pushed wavefronts, a topic that has been understudied. We raise a new conjecture related to the classical Hosono's version of the diffusive system and our numerical simulations help to confirm it, while our rigorous results only provide a partial answer.

中文翻译：

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格子 Lotka-Volterra 竞赛系统波前的速度选择

摘要 在本文中，我们研究了格子 Lotka-Volterra 竞争模型行波前的速度选择。对于线速度选择，通过构建系统的新型上解，我们广泛扩展了文献中的结果。我们证明，对于非线性速度选择，第一物种的波前在远端以更快的速率衰减。这使我们能够构建新的较低解决方案来确定推波前的存在，这是一个尚未得到充分研究的主题。我们提出了一个与经典细野版本的扩散系统相关的新猜想，我们的数值模拟有助于证实它，而我们严格的结果只提供了部分答案。