The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family covers a wide set of models used in structured population dynamics. By exploiting the stability and the monotone character of the linear ODE, we establish sufficient conditions for both the extinction of all the populations and the permanence of the system. In the case of DDEs with autonomous coefficients (but possible time-varying delays), sharp results are obtained, even in the case of a reducible community matrix. As a sub-product, our results improve some criteria for autonomous systems published in recent literature. As an important illustration, the extinction, persistence and permanence of a non-autonomous Nicholson system with patch structure and multiple time-dependent delays are analysed.
Monotone traveling wavefronts of the KPP-Fisher delayed equation
在2000年代初，Gourley（2000），Wu et al.（2001），Ashwin et al.（2002）开始研究延迟Kolmogorov-Petrovskii-Piskunov-Fisher方程的正波前。此后，该模型成为单稳态时滞反应扩散方程行波解研究中最热门的研究对象之一。本文给出了KPP-Fisher方程中单调波的存在唯一性问题的完全解。我们表明，每个单调行波可以通过迭代过程中发现。所提出的方法是基于使用特殊的单调积分算子（这是不同于通常的吴邹算子）和适当的上下解与他们相关联。对无穷远处的最终行进锋的渐近展开的分析是我们方法的另一个关键组成部分。
