具有infinite dimensional环境反馈的尺寸结构自食模型的渐近分析
Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback
摘要：
在这项工作中，我们考虑一个大小结构的同类相食模型的模型成分（生育率，增长率和死亡率）取决于大小（范围在一个无限域）和常设人口的一般功能（环境反馈）。我们的重点是系统的渐近行为，特别是对长期动态的影响的食人。为此，我们正式线性化系统的稳定状态，并建立条件的模型成分，产生一致指数稳定的执政线性半群。我们还展示了如何线性化半群生成元的点谱可以在可分离攻击率的特殊情况下表征，并建立了一个一般的不稳定性结果。进一步的谱分析使我们能够给出线性半群的异步指数增长性的条件。
英文摘要：
In this work we consider a size-structured cannibalism model with the model ingredients (fertility, growth, and mortality rate) depending on size (ranging over an infinite domain) and on a general function of the standing population (environmental feedback). Our focus is on the asymptotic behavior of the system, in particular on the effect of cannibalism on the long-term dynamics. To this end, we formally linearize the system about steady state and establish conditions in terms of the model ingredients which yield uniform exponential stability of the governing linear semigroup. We also show how the point spectrum of the linearized semigroup generator can be characterized in the special case of a separable attack rate and establish a general instability result. Further spectral analysis allows us to give conditions for asynchronous exponential growth of the linear semigroup.
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