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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 16
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Articles

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

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Pages 2920-2940 | Received 11 Jul 2017, Accepted 12 Oct 2017, Published online: 03 Nov 2017
 

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.

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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].

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