Dynamics of Delay Equations, Theory and Applications - Abstract
Otto, Andreas
For many processes in nature and technology the effects of time delays cannot be ignored and delay differential equations (DDEs) are used to describe the dynamical systems. In reality, the delays are typically not constant but rather time- or state-dependent or they are influenced to vary systematically for a better stabilization of the process. However, despite its high practical relevance, there are still open problems in the analysis of DDEs with variable delays. In this talk, I present examples from manufacturing and population dynamics, where the effects of time-varying and/or state-dependent delays are relevant. I will show that, in addition to the typical models with variable delays, these systems can be also described by DDEs with constant delays, whose theory is well-developed. I proceed by studying the question whether a DDE with an arbitrary variable delay can be transformed to a DDE with constant delay. It turns out that apart from the variable delays, which can be transformed to constant delays and are called conservative delays, there are dissipative delays, which cannot be transformed to constant delays. Finally, I demonstrate fundamental differences in the dynamics of systems with conservative and dissipative delays.