具年龄结构和非局部扩散的三种群Lotka-Volterra竞争合作系统行波解稳定性

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具年龄结构和非局部扩散的三种群Lotka-Volterra竞争合作系统行波解稳定性张丽娟, 霍振香, 任晴晴, 王福昌防灾科技学院, 廊坊 065201 Stability of the Traveling Wave Solutions for Three Species Lotka-Volterra Competitive-cooperative System with Age Structure ZHANG Lijuan, HUO Zhenxiang, REN Qingqing, WANG FuchangInstitute of Disaster-Prevention, Langfang 065201, China

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摘要本文研究一类具有年龄结构的Lotka-Volterra三种群竞争合作系统行波解存在性和稳定性.在拟单调情形下，利用解析半群和微分方程理论建立系统初值问题解R存在性及比较原理.然后，用加权能量法、比较原理等理论建立起该系统在初始扰动时除去x→-∞行波解指数衰减，证明单稳大波速行波解全局指数稳定.结果表明：行波解通常决定着初值问题解的长时间渐进行为，其稳定性揭示了种群之间竞争合作的现象，且结果能够被清晰的观测而不受外界因素干扰.

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收稿日期: 2019-04-03

PACS:	62G05
	62N01

基金资助:中央高校基本科研业务专项（ZY20215155）；河北省教育厅教改项目（2019GJJG478）和廊坊市科学技术研究项目（2017013004）；防灾科技学院教学团队建设（JT201707）资助项目.

引用本文:

张丽娟, 霍振香, 任晴晴, 王福昌. 具年龄结构和非局部扩散的三种群Lotka-Volterra竞争合作系统行波解稳定性[J]. 应用数学学报, 2021, 44(2): 251-268. ZHANG Lijuan, HUO Zhenxiang, REN Qingqing, WANG Fuchang. Stability of the Traveling Wave Solutions for Three Species Lotka-Volterra Competitive-cooperative System with Age Structure. Acta Mathematicae Applicatae Sinica, 2021, 44(2): 251-268.

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