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   RE: [xml-dev] An Exploration of Non-linear Dynamic Systems (NLDS) and XM

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Roger L. Costello wrote:

>I'll take a stab at getting things started.  First, I will 
>offer my definition of a "non-linear dynamic system".

>A non-linear dynamic system is one that changes
>in a seemingly random way.  For example, the time
>taken to process each person in line at a bank
>teller is very random - some people will have
>quick transactions and will be processed in short
>time, other people will have lengthy transactions
>and will take longer.  Thus, the system (the bank
>queue) is an example of a non-linear system.  Also, it
>is "dynamic" because the collection of people in line is 
>continually changing.  So, the bank queue is an
>example of a non-linear dynamic system.

>[Is this an accurate/reasonable definition?]


I think that this definition of NLDS is no accurate, but reasonable.  Let's
put it in caotic terms (Chaos Theory):

<quote from="Chaos, Complexity, and Entropy (A physics talk for
non-physicists), Michel Baranger.  Center for Theoretical Physics,
Laboratory for Nuclear Science and Department of Physics Massachusetts
Institute of Technology, Cambridge, MA 02139, USA and New England Complex
Systems Institute, Cambridge, MA 02138, USA MIT-CTP-3112">

A system whose con&#64257;guration is capable of changing with time is known
as a "Dynamical System". A Dynamical System consists of some "variables" and
some "equations of motion" or "dynamical equations". The variables are any
things which can vary with time. They can be multiple or single, continuous
or discrete. They must be chosen in such a way that complete knowledge of
all the variables determines uniquely the "state" of the system at one time.
In other words, two similar systems with the same values of all the
variables are in identical con&#64257;gurations now, and
will evolve identically. The set of all possible values of the variables,
i.e. the set of all possible states of the system, is called the "phase
space". The present state of the system is one point in phase space. As time
proceeds, this point moves in phase space. The job of the equations of
motion is to determine how it moves. Given the present state of the
system in phase space, the equations of motion tell you how you can
calculate the state at the next instant of time. As time evolves, this point
describes a "trajectory" or an "orbit" in phase space. If you know how to
calculate this trajectory, you say that you have solved the equations of
motion. Usually, you are given the state of the system at some initial time;
this is called the "initial conditions". Then you try to calculate the
trajectory which follows from these initial conditions.

I think that the definition of a Dynamic System in a caotic sense is more
accurate (but practical?).  However, we have to focus on *Non-Linear*
Dynamic Systems... Well, I think that Dynamic Systems, because of their
definition in the Chaos Theory, are non-linear (e. g. Calculus do not apply
in this matter of science; this systems cannot be studying applying the
fundamental concepts of calculus...)

... just some thoughts from the Chaos Theory.




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