承载能力延迟导致的间断性演变
Punctuated evolution due to delayed carrying capacity
摘要：
引入一个新的时滞方程来描述复杂非线性系统的间断演化。详细的分析和数值研究提供了所有可能类型的解决方案的人口动态的四个主要制度分别占主导地位的分类：（一）增益和竞争，（二）增益和合作，（三）损失和竞争和（四）损失和合作。我们的时滞方程在一定的参数范围内可以表现出双稳性，同时也可以表现出丰富的机制，包括单调衰减到零、平滑指数增长、间断无限增长、间断增长或交替到平稳水平、振荡接近平稳水平、持续振荡、有限时间奇点以及有限时间死亡。
英文摘要：
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a population in the four main regimes dominated respectively by: (i) gain and competition, (ii) gain and cooperation, (iii) loss and competition and (iv) loss and cooperation. Our delay equation may exhibit bistability in some parameter range, as well as a rich set of regimes, including monotonic decay to zero, smooth exponential growth, punctuated unlimited growth, punctuated growth or alternation to a stationary level, oscillatory approach to a stationary level, sustainable oscillations, finite-time singularities as well as finite-time death.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
