Behavioral finance FAQ / Glossary (Bifurcation)

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i: incidental

(critical) Bifurcation


00/6i - 01/11i - 02/4i + see chaos
theory, critical point,
emergence,
nonlinear, dynamical, cacade

At the crossroad of events,
just follow the butterfly!

Definition:

A bifurcation is a change of direction that happens when a track splits
- as a fork - in two possible ways.

It  is a typical non linear evolution seen in dynamical systems
(see that phrase).

Events, after following a rather stable path, become more chaotic,
change path after path, with imprevisible final consequences.

Those effects are all the more decisive when a chain of
successive bifurcations
leads to completely different paths.

Sorry Agatha, but Hercules Poirot was a bit absent-minded when he
failed to suspect that the legendary and perverse Amazonian butterfly,
just by flipping its wings, generated the snowstorm that stopped the
Orient Express in the Alps.

In financial markets a major bifurcation (or chain of bifurcations) takes
place when a price uptrend changes into a downtrend or vice versa.

Sometimes this broken trend entails a chaotic transition phase with high
volatility,until the new final direction becomes clear.

A typical trait of most dynamical systems

Systems with a joystick.

To drive, move, change, evolve - in other words to live -
is to choose between several paths again and again.

With free falls and sudden rises not excluded.


Bifurcations are typical of various processes in motion, thus not fully stable,
which is the definition of dynamical systems (see that phrase).

When measuring numerical data about those bifurcations,
they
show, something  of course to be expected, non linear
(see that phrase) evolutions.

In that case, preferably while keeping our eyeglasses on the nose and
our seat belt fastened, we see and feel:

Not only bent and irregular lines, that show simple

    divergences from previous situations or orientations,     

But also sudden gaps / disruptions / breaks in value and
    in nature.
And in extreme cases percolations (crucial  breakthroughs

and the emergence of new traits / features)

All this makes the bifurcation theory an important aspect of the so called
"chaos theory".

The main types of dynamical systems prone to bifurcations are:

Mathematics, when a parameter changes its value in a non linear

way (for ex. from positive to negative, or with a large non-
continuous jump).

Physical or biological systems (weather, epidemics, also nuclear
    reactions),

Human and social systems (personal life, economy, politics, arts,
    sciences..).

The last chapters of this article focus on market bifurcations,

which are measured with numerical data like prices and returns.

Types of bifurcations

From vibrations to disruptions

We can categorize bifurcations according to the importance of their
effects
.

Type

Scope

1) Small
self-corrected,
immediately
aborting,
deviations
with
negligible
effects.



 




 

 


 

 

 

 

Small short divergences happen routinely, usually with 

minor effects (see below: "when a bifurcation ...abort").

Divergences that do not change the system life
hardly meet the bifurcation definition
.

They just show a divergence - convergence dance
around a structural average state / natural pivot /
potential equilibrium.

In dynamical systems, what is called "equilibrium"
is
not full stability but includes "vibrations",
small "oscillations" that correct the balance
in a repetitive way.


In financial markets, for example, even when a
rather linear trend (uptrend, downtrend or neutral
trend) persists, there is a short term "volatility",
smallmarket prices zigzags around a "pivot" line.

We have here a gentle non linearity that swings
around a linearity
. And from time to time, a
more violent or decisive move breaks the trend
as seen below.

2) Large
deviations
/ disruptions
with
temporary
effects


Even large changes of direction or large gaps

disruptions might  be just "accidents" and get
corrected.

A tornado where it was never seen before does not
mean climatology laws changed

A market crash does not means the market
economy is dead.

3) Major /

crucial
disruptions
that change
the system

itself.





 

 




 

 

Some bifurcations, that look smooth and minor at the

start, are decisive and lead to major consequences

of the system.

Here is what is really called "bifurcation"
and more typically "chain of bifurcations"
.

Those crucial events will - immediately or in the 
long run -
not only destabilize the
system, but change
it decisively.
They alter or destroy important traits, or create
emerging ones.

Those critical bifurcations are
like the critical
thresholds of
the "percolation theory"
(see percolation)

When a bifurcation is minor or aborts,
    
with few effects on the final outcome

Storm in a glass of ...frozen water.


The mild or semi-mild cases #1 and #2 explained above are commonplace.

Many systems experience frequent bifurcations with small or temporary
effects
and many aborted bifurcations.

Those systems are said to be "robust" (or resilient).

Why is the general trend or state of things not altered in the end, or only
marginally altered, by most bifurcations?

This is because:

Either the new path is consistent with the initial one,

Or, if it really diverges, because it will "converge" again later to
   the initial state or direction.

When a minor bifurcation at the start leads
    
to a major change in the final outcome

Chain reaction leading to explosion or implosion.
Your majesty, we have here not a riot but a revolution!


On the other hand, as the case # 3 shows, it can happen that a few major
bifurcations
, including some that seem minor at the start, lead to crucial
changes and decisive evolutions.

In such cases the first bifurcation starts a chain
reaction
, as bifurcations follow
one another and
end up changing the situation completely:

1) There is a first - minor -bifurcation
     between:

--- two different
paths
.

2) The next one occurs, between:
    two
possible directions again.

This makes that the path taken
     
from the origin was among:


--- four
possible ones.

3) Then come a third bifurcation,
     the direction 
taken is thus among:  

3b) And so on: 16, 32, 64...

---

eight initial possibilities,


4) The cascade of bifurcations following the first one leads at the 
     end to a very diverging path
.

It results in a major difference of final outcome
    (the famous "butterfly wing effect").

Critical bifurcations can also appear
     after cumulative changes

Walls, floors, roofs and gates under increasing pressure.


Also, a gradual build up or decrease of pressure / energy might occur inside a
system without any apparent chain of bifurcations.

There are "underground", not too visible evolutions (see "weak signals").
Beware, they are sneaky!

After a while, they reach a critical point / tipping point /
breaking point.

=> At that point, the state, or even the nature, of the 
    
system changes - suddenly or after an unstable
     transition phase - towards a new, rather stable,
     equilibrium.

This phenomenon is a form of percolation (see that word).

It is more than a quantitative change, it is a qualitative one, with the
emergence
of new traits / features.

Common examples of changes of state

When ice becomes water, when an egg becomes a chicken.

(well, here, nothing accidental, uncertain or chaotic, just predictable,
repetitive and trite effects of regular physical and biological laws).

When a plane takes off as the appropriate speed is reached,

When the nuclear critical mass is reached and the reaction is
    self-sustaining.

But also, in economic / financial markets

When money changes direction (and pocket?)
When the economy becomes a loose cannon,
or an emerging fairy.


Major bifurcations, or major bifurcation chains, are typical phenomena in
economics and finance and in many social fields.

At the difference of some other cases mentioned above, some are relatively
unpredictable, at least in their timing.

Economics and finance - and other social systems -
are areas of uncertainty (see that word).

This goes further than a well identified probabilistic risk.

Here are some examples:

Economic evolutions

When the type of economy changes (new leading
    industries
).

Usually we have here a nonreversible chain of bifurcations,
although short lived fads can also occur.

When an economic boom leads to a slump, or a slump to a

recovery. Here things are usually reversible.


Asset market evolutions

When in a market, an information cascade gets initiated ,

does not abort and it becomes the origin of a new price trend.

In a spectacular way, when a financial bubble ends in a crash,

It is a major shock, that usually starts a chain of aftershocks.

When the image type (see image) of a stock experiences a
    decisive change,

It occurs usually as a chain of upwards or downward steps,
or sometimes through a major percolation (see that word).


Theory shifts

When a paradigm (*) breaks down and is replaced by

another theory / decision model, which until then did not
raise much interest.

(*) For example about what effect to expect from a given
      economic situation or
about the standard method to
      evaluate assets...

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