| Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays北大核心CSCD |
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| 引用本文： | 闫瑞,刘桂荣,李晓翠.Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays北大核心CSCD[J].应用数学和力学,2023,44(4):461-470. |
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| 作者姓名： | 闫瑞 刘桂荣 李晓翠 |
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| 作者单位： | 1.山西财经大学 应用数学学院，太原 030006 |
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| 基金项目： | 国家自然科学基金项目11971279国家自然科学基金项目12101034 |
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| 摘 要： | 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. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.
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| 关 键 词： | 反应扩散系统 时滞 波前解 稳定性 |
| 收稿时间： | 2022-05-23 |
Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays |
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| Yan R.,Liu G.,Li X..Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays[J].Applied Mathematics and Mechanics,2023,44(4):461-470. |
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| Authors: | Yan R Liu G Li X |
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| Affiliation: | 1.School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, P.R.China2.School of Mathematical Sciences, Shanxi University, Taiyuan 030006, P.R.China3.College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P.R.China |
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| 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. |
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| Keywords: | delay reaction-diffusion system stability traveling wavefront |
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