Traveling Waves of a Delayed Differential System in a Lattice
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摘要: 针对部分种群个体活动而其他个体静止的单种群模型, 主要研究了一维格上具有静止阶段的时滞反应扩散系统的行波解的定性性质.在单稳和拟单调的假设条件下, 首先,研究了行波解的存在性.其次, 证明了行波解的渐近行为、 单调性以及唯一性.最后, 证明了所有非临界波前解(即波速大于最小波速的波前解)是指数渐近稳定的.Abstract: The qualitative properties of traveling waves of a delayed differential system in a lattice with a quiescent stage were addressed. Under monostable and quasi-monotone assumptions, the existence of the traveling wave solutions were first established. Then, the asymptotic behavior, monotonicity and uniqueness of all wave profiles were proved. The exponential asymptotic stability of all non-critical traveling fronts was finally proved.
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Key words:
- traveling wave solution /
- lattice differential system /
- quiescent stage /
- delay
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