Linear vs. nonlinear speed selection of the front propagation into unstable states

TL;DR

This paper investigates the speed selection problem in the classical Lotka-Volterra competition system, providing a new necessary and sufficient condition that clarifies the underlying mechanisms of wave propagation into unstable states.

Contribution

It introduces a novel criterion for speed selection in the Lotka-Volterra system, linking decay rates of traveling waves to the selection process.

Findings

Established a new necessary and sufficient condition for speed selection.

Linked decay rates of minimal traveling waves to the selection mechanism.

Revealed the fundamental nature of linearly selected speeds in monostable systems.

Abstract

In this paper, we mainly consider the speed selection problem for the classical Lotka-Volterra competition system. For the first time, we propose a sufficient and necessary condition for this long-standing problem from a new point of view. Moreover, our results can also reveal the essence of the linearly selected problem for the monostable dynamical system from the observation of the decay rate of the minimal traveling wave solution.