Stability and Traveling Fronts in Lotka-Volterra Competition Models with Stage Structure
Stability and Traveling Fronts in Lotka-Volterra Competition Models with Stage Structure
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DOI：
10.1137/s0036139902416500
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
J. Al-Omari;S. A. Gourley
中科院分区：
文献类型：
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作者：
J. Al-Omari;S. A. Gourley
本文研究了两个种群相互作用的时滞微分方程模型，其中两种群的成年成员处于竞争状态。的竞争效应是洛特卡-沃尔泰拉的那种，在没有竞争的情况下，它是假设每个物种的发展根据一个简单的年龄结构模型，减少到一个单一的方程的总成年人口的预测。对于两个物种中的每一个，模型都包含了一个时间延迟，它代表了该物种从出生到成熟的时间。这样，在成年人的补充项中就出现了时滞。确定了模型的动力学，并对每个平衡点建立了全局稳定性结果。该模型的平衡点包含成熟时滞。研究了该模型的反应扩散推广，当每个种群中只有成年个体可以扩散时，该模型的全局收敛性是很强的.我们证明了一个...
This paper is concerned with a delay differential equation model for the interaction between two species, the adult members of which are in competition. The competitive effects are of the Lotka--Volterra kind, and in the absence of competition it is assumed that each species evolves according to the predictions of a simple age-structured model which reduces to a single equation for the total adult population. For each of the two species the model incorporates a time delay which represents the time from birth to maturity of that species. Thus, the time delays appear in the adult recruitment terms.The dynamics of the model are determined, and global stability results are established for each equilibrium. The equilibria of the model involve the maturation delays. The criteria for global convergence to each equilibrium are sharp and involve these delays.A reaction-diffusion extension of the model is also studied for the case when only the adult members of each species can diffuse. We prove the existence of a ...