Overview: The Dynamics of Complex Systems

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Overview: The Dynamics of Complex Systems

Yaneer Bar
-
Yam


Definition:


Complex: Consisting of interconnected or interwoven parts; we must understand not only
the behavior of the parts but how they act together to form the behavior of the whole. We
cannot
describe the whole without describing each part, and because each part must be
described in relation to other parts, that complex systems are difficult to understand.


Universal principles and tools guide and simplify our inquiries in to the study of
speci
fics. For the study of complex systems, universal simplifications are particularly
important.


Properties of Complex Systems
; Function, Structure, Diverse Manifestation, Time,
Change, Growth, Death, Adaptation




Elements (and their Number)



Interactions (a
nd their Strength)



Formation/Operation (and their Time Scales)



Diversity/Variability



Environment (and its demands)



Activity(ies) and its [their] objective(s)


Emergence:


How is the complexity of the whole related to the complexity of its parts?


Emergent
Complexity: a system composed of simple parts where the collective behavior
is complex. The behaviors of many simple parts interact in such a way that the behavior
of the whole is complex. (atoms)


Emergent Simplicity: A system composed of complex par
ts where the collective
behavior is simple. (planet orbiting a star)


In terms of scale, in which one view the systems is complex, but in another frame of
reference the system behaves in simple actions.


Complexity:


Defining quantitatively
what we mean b
y complexity. Information theory and
computation theory is used to describe complex systems quantitatively.


Complexity is the amount of information necessary to describe a system.


Questions:

1.

Space: Structure and substructure

2.

Time: Time intervals, Respon
se

3.

Self
-
organization and/versus organization by design: Existence, Development
guides

4.

Complexity: Define, Variance of Complexity


Methodology:


Purpose: to extract general principles. Thereby utilizing and developing mathematical
models.




Don’t take it a
part. Theoretical analytical methods; mean field approach enable
parts of a system to be studied in context.



Don’t assume smoothness.

Static Models, Dynamical Models, Interactive Maps
and Cellular Automata.



Don’t assume that only a few parameters are imp
ortant. Computer simulations
keep track of many parameters and may be used in the study of dynamical
processes.


Two Methods:


1.

A specific system is selected and each of the parts as well as their interactions are
identified and described. The objective i
s to show how the behavior if the whole
emerges from them.

2.

The second approach considers a class of systems, where the essential
characteristics of the class are described, and statistical analysis is used to obtain
properties and behaviors of the systems.


* the two major concepts of this chapter are the definitions and descriptions of
emergence and complexity as well as the tools used to identify their characteristics in
complex systems. Most importantly here, is quantitatively.