Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion

Math Biosci Eng. 2017;14(5-6):1187-1213. doi: 10.3934/mbe.2017061.

Abstract

This paper is concerned with invasion entire solutions of a monostable time periodic Lotka-Volterra competition-diffusion system. We first give the asymptotic behaviors of time periodic traveling wave solutions at infinity by a dynamical approach coupled with the two-sided Laplace transform. According to these asymptotic behaviors, we then obtain some key estimates which are crucial for the construction of an appropriate pair of sub-super solutions. Finally, using the sub-super solutions method and comparison principle, we establish the existence of invasion entire solutions which behave as two periodic traveling fronts with different speeds propagating from both sides of x-axis. In other words, we formulate a new invasion way of the superior species to the inferior one in a time periodic environment.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Animals
  • Diffusion*
  • Ecosystem
  • Humidity
  • Models, Biological*
  • Models, Statistical
  • Population Dynamics*
  • Predatory Behavior*
  • Temperature
  • Time Factors