Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays

YAN Rui; LIU Guirong; LI Xiaocui

doi:10.21656/1000-0887.430172

Volume 44 Issue 4

Apr. 2023

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YAN Rui, LIU Guirong, LI Xiaocui. Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays[J]. Applied Mathematics and Mechanics, 2023, 44(4): 461-470. doi: 10.21656/1000-0887.430172

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Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays

doi: 10.21656/1000-0887.430172

YAN Rui^1
,,
LIU Guirong²,
LI Xiaocui^{3
,
,}

1.
School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, P.R.China
2.
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, P.R.China
3.
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P.R.China

Received Date: 2022-05-23
Rev Recd Date: 2022-06-28
Publish Date: 2023-04-01

Abstract

Abstract

The stability of traveling wave solutions of the reaction diffusion model is a very important research topic. The globally nonlinear stability of traveling wavefronts for a discrete cooperative Lotka-Volterra system with delays was studied. More precisely, for the initial perturbation decaying exponentially to the traveling wavefronts with a relatively large speed at infinity, but arbitrarily large speeds in other positions, by means of the L²-weighted energy method, the comparison principle and the squeezing technique, such traveling wavefronts were obtained and proved to be of exponentially asymptotic stability. Moreover, the problem of establishing the energy estimates was solved under the actions of the discrete dispersal operator and the time delays. In short, the extension of the weighted energy method to discrete systems with delays, enriches the relative research.
- reaction-diffusion system,
- delay,
- traveling wavefront,
- stability

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References(30)

References

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