Discrete N-barrier maximum principle for a lattice dynamical system arising in competition models
Journal
Discrete and Continuous Dynamical Systems- Series A
Journal Volume
40
Journal Issue
1
Pages
153-187
Date Issued
2020
Author(s)
Abstract
In the present paper, we show that an analogous N-barrier maximum principle (see [3,7,5]) remains true for lattice systems. This extends the results in [3,7,5] from continuous equations to discrete equations. In order to overcome the difficulty induced by a discretized version of the classical diffusion in the lattice systems, we propose a more delicate construction of the N-barrier which is appropriate for the proof of the N-barrier maximum principle for lattice systems. As an application of the discrete N-barrier maximum principle, we study a coexistence problem of three species arising from biology, and show that the three species cannot coexist under certain conditions.
Type
journal article