论文标题
D-Concave非自治标量的临界过渡出现在人口动态中的普通微分方程
Critical Transitions in D-Concave Nonautonomous Scalar Ordinary Differential Equations Appearing in Population Dynamics
论文作者
论文摘要
具有有限渐近极限的功能会导致“过去系统”和“未来系统”之间的过渡方程。在非自治的强制非线性标量的普通微分方程中，相对于状态变量，对这个问题进行了分析。基本的假设是存在三种双曲线解决方案，在这种情况下，上层和下部是有吸引力的。所有全局动力学可能性都是用回调吸引子的内部动力学来描述的：可能会出现两个双曲线有吸引力的解决方案或缺乏IT（小费）的情况。这种分析以过程的语言以及问题的偏压制定，包括速率诱导的临界过渡的情况以及相诱导的和大小引起的小费的情况。这些结论应用于数学生物学和种群动态模型。描述了速率诱导的跟踪现象，导致本地物种灭绝或侵袭非本地物种，以及受刺激的III型功能响应影响的人群模型可能会发生由于过渡量的变化而引起的倾斜。在所有这些情况下，临界过渡的出现都可以理解是由于质量效应的力量。
A function with finite asymptotic limits gives rise to a transition equation between a "past system" and a "future system". This question is analyzed in the case of nonautonomous coercive nonlinear scalar ordinary differential equations with concave derivative with respect to the state variable. The fundamental hypothesis is the existence of three hyperbolic solutions for the limit systems, in which case the upper and lower ones are attractive. All the global dynamical possibilities are described in terms of the internal dynamics of the pullback attractor: cases of tracking of the two hyperbolic attractive solutions or lack of it (tipping) may arise. This analysis, made in the language of processes and also in terms of the skewproduct formulation of the problem, includes cases of rate-induced critical transitions, as well as cases of phase-induced and size-induced tipping. The conclusions are applied in models of mathematical biology and population dynamics. Rate-induced tracking phenomena causing extinction of a native species or invasion of a non-native one are described, as well as population models affected by a Holling type III functional response to predation where tipping due to the changes in the size of the transition may occur. In all these cases, the appearance of a critical transition can be understood as a consequence of the strength of Allee effect.
