Dynamical system

Dissipative system

A dissipative system is a dynamical system which is contracting for all but finitely many points, i.e. nearly all infinitesimal balls of initial conditions shrink over time.¹ #m/def/dynamics A distinct but related class of system is the Conservative system.

Characterization

Differential system

For a differential system the evolution of an infinitesimal volume follows

and dissipative dynamics is characterised by lim𝑡→∞𝑣(𝑡) →0.

Iterated map

For an Iterated map the evolution of an infinitesimal volume follows

and again dissipative dynamics is characterised by lim𝑛→∞𝑣𝑡𝑛 =0.

Properties

The phase space of a dissipative system is populated by attractors and may be divided into basins of attraction.

#state/develop | #lang/en | #SemBr