Dynamical systems

Abstract

We give the definition of dynamical system and a classification of such systems: finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous and discontinuous systems; autonomous and non-autonomous systems; and composite systems. Classes of finite-dimensional dynamical systems that we address include systems determined by ordinary differential equations, ordinary differential inequalities, ordinary difference equations, and ordinary difference inequalities. General classes of infinite-dimensional dynamical systems that we address include systems determined by differential equations and inclusions defined on Banach spaces and systems determined by linear and nonlinear semigroups. Specific classes of infinite-dimensional dynamical systems that we address include systems determined by functional differential equations, Volterra integrodifferential equations, and certain classes of partial differential equations. For all cases, we present specific examples.