Bistable waves for two species competition systems in a periodic discrete habitat

Shiheng Fan; Xiao-Qiang Zhao

doi:10.3934/dcds.2025060

Article Contents

2025, Volume 45, Issue 11: 4349-4387. Doi: 10.3934/dcds.2025060

This issue Previous Article Multiple periodic solutions for coupled asymptotically linear wave equations with variable coefficients Next Article Global existence and regularity in a three-dimensional Keller-Segel-Navier-Stokes system with indirect signal production

Bistable waves for two species competition systems in a periodic discrete habitat

Shiheng Fan^, and
Xiao-Qiang Zhao

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada

^*Corresponding author: Shiheng Fan
^*Corresponding author: Shiheng Fan

Received: December 2024

Revised: April 2025

Early access: May 7, 2025

Published online: May 7, 2025

The first author is supported in part by China Scholarship Council (202207970008). The second author's research was supported in part by the NSERC of Canada (RGPIN-2019-05648 and RGPIN-2025-04963).

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Abstract

In this paper, we study bistable traveling waves for a Lotka–Volterra two species competition system in a periodic discrete habitat. Under appropriate assumptions, this lattice system with periodic initial data admits a bistable structure. We then establish the existence and uniqueness of the pulsating wave front connecting two stable semi-trivial equilibria and the global stability of such a bistable wave for wave-like initial data. We also obtain sufficient conditions to determine the sign of the bistable wave speed. Finally, we present an application example and numerical simulations.

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Mathematics Subject Classification: 34A33, 34C12, 37C65, 92D25.

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Figure 1. Initial time and long time behaviour of both species for period 3 and 4 with wave-like initial values

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Figure 2. Cross sections for the initial time and ultimate time of both species for wave-like initial condition

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Figure 3. Initial time and long time behaviour of both species for period 3 and 4 with wave-like initial values

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Figure 4. Cross sections for the initial time and ultimate time of both species for wave-like initial condition

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Figure 5. Initial time and long time behaviour of both species for period 3 and 4 with wave-like initial values

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Figure 6. Cross sections for the initial time and ultimate time of both species for wave-like initial condition

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