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Dates of related message(s) in the
Behavioral-Finance group (*):
Year/month, d: developed / discussed,
i: incidental

Dynamical systems



00/11i - 01/1i + see self-adaptable
market, bifurcation,
chaos theory,
percolation, evolutionary economics,
uncertainty,random walk, emergence,
(dynamical) equilibrium + bfdef3

Living things move and change.
If they don't, they are not living things.

Most systems, natural or man-made, move and change also.
If not they are dormant, inert or ...dead systems
.

Wherever you walk, be ready to meet changes at every step!

Definition (dynamical system):

Mathematicians define dynamical systems as processes in
motion.

Definition (complex dynamical system):

Complex dynamical systems are systems in which many
factors
interact ( complexity)
and create ceaseless, minor or major, changes.

Nature, life, the human being, and human societies 
    (this includes economic 
activities) are complex dynamical systems.

They never rest!
They never stay the same! History is full of surprises!

Their state is ever changing , which is the
definition of "dynamic".

This is due to many interactions (complexity),
whether or not they can be translated into mathematical models.

Markets are (complex) dynamical systems.

Every day is a new market day, with new transactions, new
quantities, new prices.

Instability and disequilibrium

Restless or lawless?

We can find three, quite different cases of
"mobile" systems: linear, random, uncertain


1) The most simple ones follow a stable, linear,
    continuous trajectory
,

They obey some easy to predict law of inertia, with few chances
(but not zero chances) that an accident might perturb it.


2) Others are less linear, they involve small irregularities /

 disruptions, but obey rather closely a precise
  random probability law.

Those laws help predict things, at least if they can be trusted
(see "rare events" and "fat tails", which probability, in
"dynamical systems"
, are higher than those laws predict, and
more generally the "numeracy bias" ...)


3) But many others have rather unstable traits.

Their main traits and behaviors change with time.

This happens through (see those words):

Bifurcations


(taking a new direction

disruptions
Non linear

(gaps)

Percolations


(changes of nature,
           emerging traits)

Those events express the "perfect", more or less "chaotic",
dynamical system in which:

Uncertainty predominates over clear probabilities.

Dynamic means:
    - unbalanced-rebalanced,
    - disorganized-reorganized,
    - progressing-regressing,
    - emerging-aborting.

Some self-correcting mechanisms might stabilize things, but not always.

Some changes are temporary,

Oothers on the contrary bring

robust / decisive / irreversible traits.

They cause real evolutionary / Darwinian disruptions / mutations that create
new traits and effects (see evolutionary, emergence, bifurcation, percolation....).

Dynamical systems belong mostly to the realms of
disequilibrium, quasi-equilibrium or semi-stability.

Even the appellation "dynamical equilibrium" would
be misleading, as things rarely adjust exactly.

The word equilibrium is more an attribute of static systems in which things
do not move.

We can talk here about degrees of stability / instability:

When changes
    are
minor and

gradual:


 

 

The system is rather stable and "robust",

with only small "vibrations" (volatility).

Or, when a system is usually instable, there is
a temporary "stasis" (near static phase).

The beast is at rest and quietly digesting!

When they
    enter a
fully

disorganized
state
with
unclear
orientation:


We get a "chaotic (*)
     phase"
until a new, stabler,
state is found.

(*) As dynamical systems theorists call it.

Whence the "chaos theory", as the
dynamical system theory is sometimes
called.

What kind of changes is it about?
     How deep can they be?

Minor shifts or major earthquakes?

Changes in dynamical systems take various degrees and shapes.
They can be:

Minor, smooth, gradual

Or

Large, abrupt, non-linear (see that
word), moves,

Bringing major
evolutions

Or

Self-correcting around a quasi
equilibrium
,

Quantitative additions
or reductions

 

 




Or



 

 

 

Qualitative / disruptive changes.

Here we have a "percolation" (see
that word) from a state to another,
with emerging, or disappearing,
traits.

In some cases in can even be an
irreversible mutation, a change of
nature of the system or organism.

Regressive, "entropic"
like in thermodynamics,
giving a poorer, less
organized, less stable
situation

Or




Creative, "negentropic", leading
to a more complex,
organized,
enriched situation, with emergence
(see that word) of new traits when
an
evolution threshold is crossed.

Markets, as examples of
     (complex) dynamical systems

Ready for the market rock and roll?

Theories of economic equilibrium were the fashions a few
decades ago, peppered with mathematics from the world of physics.

But such beliefs suppose a static and close-ended environment.

Those equilibrium-based models cannot fully reflect the real economic world.

=> When they are still used, it is only as approximations.

Free / open markets, such as stock markets for example, show ever
changing equilibriums
, thus are typical of dynamical systems (cum
complexity, as many factors interrelate).

Often, those market changes take the form of

(irregular) alternations of different types of phases:

Chaotic / transition phases

(high price volatility with no clear trend).


Semi-stable phases (persistent upwards / downwards or
    horizontal
trends, with just a small volatility swing around the

 moving or stable average).

Among those quasi regular trends, horizontal ones, called
"stases"
, are of course the epitome of stability.

Are markets examples of randomness?

Or of chaos?
Or of adaptation, evolution and self-organization?

Wild West? Law and order?
Or just life adaptation?

Chaos might seem to obey fully the simple laws of randomness (see
distribution curve, RWH) but is thought to be deterministic in essence.

On the other hand, markets do not obey fully those random probability
laws, they differ as:

Self-organization (see percolation) plays a part.

their dynamics make them complex adaptable systems in which only the 
  
fittest players obtain a sustainable success (see "evolutionary economics").

The everyday / short term reality in markets brings a lot of uncertainty /

ambiguity (see uncertainty vs. risk) to this mix of randomness / non
randomness.

Markets are more uncertain than only risky.

They illustrate the difference between:

Risk

Risk is normally something predictable, based on
solid statistical probabilities (well, solid as long
as the "stable phase" last, as it can suddenly break
tomorrow)

Uncertainty

 



(when the "chaotic phase", explained above,
strikes or might strike),

Uncertainty (see that word) relates to
occurrences that cannot be really
measured in advance
.

Here, historical probabilities are not fully
efficient predictors.
What can only help is to imagine scenarios and
to use fuzzy logic or Bayesian probabilities.

(*) To find those messages: reach that BF group and, once there,
      1) click "messages", 2) enter your query in "search archives".

Members of the BF Group, please
 vote on the glossary quality at BF polls

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