Hi

I will try to relate those terms. The following is nothing you can readAre complex systems nothing more than a system of chaotic equations?

Similiar to the system of equations used in linear algebra and matrices

in a book or article. It is so to say my interpretation of things I have

read. I also checked the Wikipedia-articles, which are okay. I first try

to be mathematical, then I give some "intuitive" interpretation or examples.

the math

complex systemsare given by a number of entities (variables x_1(t),x_2(t), ...),

which are connected non-linearly, e.g. d x_1(t) / d_t = -x_1(t)^2 * x_2(t)... plus

similar equations for x_2(t) etc, where "t" can be interpreted as the time.

Note that if you set x_2(t)=x_3(t)=...=1 you will recover something like a marginal

version of the logistic map (just discretise time).

The study of thosecomplex systemsis calledsystem theory.

Mathematically, one is interested in two different things: fixed points and dynamics.

- A fixed point is a set of specific values of x_1(t), x_2(t), such that they do not

change while further evolving the system in time.

- Then, the dynamics could be such that certain values of x_1(t), x_2(t) etc. are

repeated periodically (or in another similarity pattern).

- Further, the dynamics could be that no such similiarity pattern can be found. Then,

the complex system is called"chaotic".

interpretation etc.

Since the dynamics of complex systems is difficult to control, one may

perform simulations. Typically, so-calledmulti-agent systems/cellular automata

are used. Why?

A complex system can be understood as a set of individuals, who interact

with each other. Thus, the reference to the "Game of Life" above. They may

adapt their strategy (calledcomplex adaptive systems) or not.

For example, Psychologists have invented a "multi-agent system" called the

"Cybernetic model": since one cannot "calculate" why certain animals form

certain "societies", one invented a model, which controls the movements of

an animal based on some interactions with the environment. Thus, the way

how animals herd, allows to extract information about the "character" of

the animals. The same, in some limits, is also possible for human beings.

For example, Blackjack players (me ) have tried to model interaction to

extract the optimal game strategy. In the end, several millions of games have

been played using computer simulations.

For example, the stock market: shared/derivatives etc. show a certain time history,

which can be analysed. Typical properties of complex (adaptive) systems, like memory

and "fat tails" in the distribution can be seen. All this can be interpreted in

the context of a "multi-agent system".

etc.etc.

It even can be a way to analyse"network traffic", and hence, security: you have

entities, which interact with each other. Having a "baseline", you may detect deviations.

In some context of interpretation, we here even may talk of a reference monitor.

Cheers