Global stability of traveling wave fronts for a reaction–diffusion system with a quiescent stage on a one-dimensional spatial lattice

ABSTRACT

This paper is concerned with the stability of traveling wave fronts for a coupled system of non-local delayed lattice differential equations with a quiescent stage. It shows that under certain conditions all non-critical traveling wave fronts are globally exponentially stable, and critical ftraveling wave fronts are globally algebraically stable by applying the weighted energy method and the semi-discrete Fourier transform.

Keywords:

• Global stability
• lattice differential equation
• weighted energy method
• comparison principle
• semi-discrete Fourier transform

AMS Subject Classifications:

• 35B40
• 35K57
• 35R20
• 92D25

Acknowledgements

The authors are grateful to the referees for their valuable suggestions that help improvement of the manuscript.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is supported by NSF of China [grant number 11301121], [grant number 11772203]. The third author is supported by NSF of China [grant number 11361047]; and NSF of Qinghai Province [2012-Z-910].