Delayed feedback mechanisms

许多真实的世界过程将其自身输出的一部分作为输入反馈给自身。例如，在气候系统中，有一些机制可以放大或缩小气候最初驱动因素的影响。由于子系统之间的相互作用往往不是瞬时的，预测和忠实的数学模型的系统反馈应包括过去的依赖。实际上，延迟微分方程是许多具有实际意义的历史驱动问题的确定性数学模型，延迟微分方程可以看作是无限维动力系统。虽然有各种各样的分析，几何和计算技术来研究动力学延迟微分方程，有许多具有挑战性的开放性问题。例如，在Mackey-Glass方程中数值观测到的混沌的存在性尚未得到证明。该项目的目的是研究具有不同类型时滞的非线性微分方程的动力学，如多重时滞、时间依赖时滞和状态依赖时滞。

Many real world processes feed parts of their own outputs back to themselves as inputs. For instance, in the climate system there are mechanisms that can either amplify or diminish the effects of the initial drivers of climate. Since interactions between subsystems are often not instantaneous, predictive and faithful mathematical models of systems with feedback should incorporate past dependence. Indeed, delay differential equations are deterministic mathematical models of many history driven problems of practical importance.Delay differential equations can be viewed as infinite dimensional dynamical systems. Although there is a wide variety of analytical, geometric and computational techniques to study the dynamics delay differential equations, there are many challenging open questions. For instance, the existence of the numerically observed chaos in the Mackey-Glass equation has not been proved yet. The aim of the project is to study the dynamics of nonlinear differential equations withdifferent types of time lags such as multiple, time-dependent and state-dependent.