出生时状态为分布的分层结构种群的稳态
Steady states in hierarchical structured populations with distributed states at birth
摘要：
研究了一类拟线性一阶双曲型偏积分微分方程的定态解。该模型描述了一个出生时状态分布的分层结构种群的演化。等级规模结构模型描述了个体经历特定规模环境时的种群动态。例如，在一个种群中，个体表现出同类相食的行为，成为猎物（或攻击）的机会取决于个体的大小。该模型的另一个显著特征是个体以任意大小被招募到群体中。这相当于一个无限秩的积分算子描述的招聘过程。首先，我们建立了该模型存在正平衡态的条件。我们的方法利用了巴拿赫空间锥壳中非线性映射的不动点结果。然后利用巴拿赫格上正算子理论的结果，研究了增长率可分的特殊情形下定态的稳定性。
英文摘要：
We investigate steady states of a quasilinear first order hyperbolic partial integro-differential equation. The model describes the evolution of a hierarchical structured population with distributed states at birth. Hierarchical size-structured models describe the dynamics of populations when individuals experience size-specific environment. This is the case for example in a population where individuals exhibit cannibalistic behavior and the chance to become prey (or to attack) depends on the individual's size. The other distinctive feature of the model is that individuals are recruited into the population at arbitrary size. This amounts to an infinite rank integral operator describing the recruitment process. First we establish conditions for the existence of a positive steady state of the model. Our method uses a fixed point result of nonlinear maps in conical shells of Banach spaces. Then we study stability properties of steady states for the special case of a separable growth rate using results from the theory of positive operators on Banach lattices.
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