具有年龄结构的Lotka-Volterra竞争系统行波解的稳定性

Stability of Traveling Wave Fronts for Delayed Lotka-Volterra Competition Systems With Stage Structures

主要研究了一类具有年龄结构的Lotka-Volterra竞争系统行波解的稳定性.在拟单调的情形下,利用解析半群理论和抽象泛函微分方程理论,首先建立起系统初值问题的解在R上的存在性和比较原理.然后基于加权能量法、比较原理和嵌入定理,建立起该系统在大初始扰动(即除去当x→-∞时在行波解附近的初始扰动是指数衰减的,在其他位置的初始扰动可以任意大)下,单稳大波速行波解的全局指数稳定性.研究结果表明,行波解作为系统的稳态解,通常决定着初值问题解的长时间渐近行为.其稳定性揭示了种间竞争的现象和结果能够被清晰地被观测到,而不受外界因素的干扰.

The stability of traveling wave solutions to a class of Lotka-Volterra competitive systems with age structures was studied. In the case of quasi-monotonicity,the existence and comparison theorems for the solutions to the initial value problems of the systems were first established on R with the analytic semigroup theory and the abstract functional differential equations. Then based on the weighted energy method,the comparison theorem as well as the embedding theorem,the global exponential stability of the monostable large-speed traveling wave solutions under the so-called large initial perturbation（ i.e. the initial perturbation around the traveling wave decaying exponentially as x→-∞,but being arbitrarily large at other locations） was obtained for the systems in the weighted Sobolev space.The results show that,as the steady state solution of the system,the traveling wave solution usually determines the long-term asymptotic behavior of the solution to the initial value problem. Its stability reveals that the phenomena and results of inter-species competition systems can be clearly observed without interference by external factors.