Spreading speed of a lattice time-periodic Lotka–Volterra competition system with bistable nonlinearity

Abstract

We study the uniqueness and sign of bistable wave speed for a lattice time-periodic Lotka–Volterra competition system of bistable type. The sign of wave speed reflects the propagation direction of traveling wave which arises as a challenging problem in the field of traveling wave theory. Actually, even for the case of homogeneous environment, there is no common method that can be used to deal with it. First, we show that the speed of the bistable wave of the model is unique. Second, by making use of upper–lower solution method and comparison principle, a set of explicit conditions is built up such that the sign of the wave speed can be justified. From the viewpoint of biology, these conditions reveal which of the species will tend to extinction and which will survive when the environment changes periodically in time.

Keywords:

• Propagation direction
• periodic traveling wavefronts
• lattice Lotka–Volterra competition system
• heterogeneous environment

2020 Mathematics Subject Classifications:

• Primary: 35K57
• 35B20
• 92D25

Acknowledgements

We would like to thank the anonymous referees for careful reading and many valuable comments that have helped greatly improve the exposition of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the Scientific Research Fund of Hunan Provincial Education Department grant (20B512) and the Natural Science Foundation of Hunan Province grant (2021JJ30019). This work is partially supported by the National Natural Science Foundation of China grant (11626129 and 11801263), the Natural Science Foundation of Hunan Province grant (2018JJ3418) and Hunan Key Laboratory of Mathematical Modeling and Scientific Computing.