Dynamical System Theory

FoodSim'08, 2008

The dynamical system approach characterizes a system by its state and models its evolution by a transition function (or a relation). This approach is widely used in system's simulation and there exists several formalisms used to describe a dynamical system: ordinary differential equations, partial differential equations, iterated equations (finite set of coupled difference equations), cellular automata, etc., following the discrete or continuous nature of the time, the space and the value used in the modelling.

International Journal of Applied Mathematical Research, 2012

Dynamical system is a young and vigorously growing area of research which promises enormous potential and opportunities. This paper aims to introduce some of the preliminary concepts of dynamical systems. Many application sides of the subject are noted to encourage the reader for future developments. Resources are supplied in the references for further reading.

2007

One approach starts from time-continuous differential equations and leads to time-discrete maps, which are obtained from them by a suitable discretization of time. This path is pursued, eg, in the book by Strogatz [Str94]. 1 The other approach starts from the study of time-discrete maps and then gradually builds up to time-continuous differential equations, see, eg,[Ott93, All97, Dev89, Has03, Rob95].

Journal of Differential Equations, 2008

In this paper we consider dynamical systems generated by a diffeomorphism F defined on U an open subset of R n , and give conditions over F which imply that their dynamics can be understood by studying the flow of an associated differential equation,

2005

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2012

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Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2013

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