人口规模结构：移民、（双）稳定性和净增长率
Size-structured populations: immigration, (bi)stability and the net growth rate
摘要：
考虑一类生理结构种群模型，该模型为一阶非线性偏微分方程，具有非局部边界条件，种群外部流入为常数.我们证明了线性化系统是由一个拟压缩半群。我们还建立了平衡解的线性稳定性是由一个广义净再生函数。在一个特殊情况下的模型成分，我们讨论的非线性动力学系统时，线性化的操作员的谱界等于零，即当线性化不决定稳定。这使我们能够通过一个具体的例子来证明移民如何可能对人口有益。特别是，我们表明，从一个非线性不稳定的正平衡的线性稳定和不稳定的平衡对分叉。事实上，线性化系统表现出双稳态，为一定的值域的值的外部流入，潜在的Allée效应引起的。
英文摘要：
We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by Allée-effect.
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