Delayed feedback mechanisms

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 with
different types of time lags such as multiple, time-dependent and state-dependent.