Delay Differential Equations

Delay Differential Equations (DDEs) are mathematical equations that describe how a system changes over time, taking into account that the effects of past states influence current behavior. Unlike standard differential equations, which depend only on the current state, DDEs incorporate delays—meaning the outcome at a certain time relies on information from previous times. This concept is important in various fields, such as biology, engineering, and economics, where processes naturally have a time lag, like a population responding to past food availability or a mechanical system reacting to previous motions.