Then we have a finite discrete dynamical system
For example, in the study of discrete dynamical systems
 or continuous time dynamical systems [6, 7], a positive solution for a system of equations represents the existence of stationary states.
Although the theory of continuous- and discrete-time dynamical systems as presented in the literature is different, the analysis of time scales is nowadays recognized as a right tool to unify the seemingly separate fields of discrete dynamical systems
Discrete dynamical systems
and chaotic machines; theory and applications.
It covers current research on such discrete dynamical systems
as one and two- dimensional cellular automata and illustrates how these systems can be used for artistic purposes by translating their mathematical configurations into visual media and music.
Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems
and describing chaotic systems.