Studying delay differential equations is motivated by the fact that the evolution of systems in physics, chemistry, the life sciences, engineering, and economics, may, and often does, depend not only on the present state of the system but also on earlier states. Examples arise from the 2-body problem of electrodynamics (which is barely understood), in laser physics, materials with thermal memory, biochemical reactions, population growth, physiological regulatory systems, and business cycles, among many others. Delays may also appear when one wants to control a system by applying an external force which takes into account the history of the solution. Also mathematical problems in geometry and probability yield delay differential equations.
In modeling real world phenomena another important aspect is uncertainty. It is often useful to take into account some randomness or environmental noise. This Special Issue addresses both aspects of dynamical systems, namely, hereditary characteristics and stochasticity. We have selected a dozen of papers which illustrate some lines of recent research.
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