yums seminar series
System Delay as a Feature, Not a Bug
Lauren Lazarus Melfi
Differential equations, used to describe how quantities evolve in time, are generally assumed to rely on the current state of the system to determine where it will go next. However, in realistic contexts, there is a delay between events and their effects, since information takes time to travel and the system may need time to process the information and react appropriately. So how does this delay affect systems’ behavior? The presence of delay in a differential equation allows for a much richer set of behaviors in the solutions, as the solution set becomes infinite-dimensional. In particular, the delay can create periodic motion, even in very simple-looking first-order differential equations. We explore the nature and frequency of these oscillations and the possibility of resonance and synchronization with other oscillating agents.