Traveling wave fronts in a delayed lattice competitive system

Abstract

This paper is concerned with the existence, asymptotic behavior, strict monotonicity, and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed lattice competitive system. We first prove the existence of traveling wave fronts by constructing upper and lower solutions and Schauder’s fixed point theorem, and then, for sufficiently small intraspecific competitive delays, prove that these traveling wave fronts decay exponentially at both infinities. Furthermore, for system without intraspecific competitive delays, the strict monotonicity and uniqueness of traveling wave fronts are established by means of the sliding method. In addition, we give the exact decay rate of the stronger competitor under some technique conditions by appealing to uniqueness.

Keywords:

• Delayed lattice competitive system
• traveling wave front
• asymptotic behavior
• uniqueness
• upper and lower solutions

AMS Subject Classifications:

• 35B40
• 34K31
• 34K10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Kun Li was supported by the National Natural Science Foundation of China [grant number 11401198]; the Hunan Provincial Natural Science Foundation of China [grant number 2015JJ3054]; the Project Funded by China Postdoctoral Science Foundation [grant number 2015M582882]; the A Key Project Supported by Scientific Research Fund of Hunan Provincial Education Department [grant number 14A028]; the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province. Jianhua Huang was supported by the National Natural Science Foundation of China [grant number 11371367]. Xiong Li supported by the National Natural Science Foundation of China [grant number 11571041]; the Fundamental Research Funds for the Central Universities.