Behavioral finance FAQ / Glossary (Bifurcation)
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theory, critical point, emergence,
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At the crossroad of events,
just follow the butterfly!
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
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
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-
Physical or biological systems (weather, epidemics, also nuclear
Human and social systems (personal life, economy, politics, arts,
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
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 /
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.
Even large changes of direction or large gaps/
disruptions might be just "accidents" and get
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 /
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
Those critical bifurcations are
like the critical thresholds of
the "percolation theory"
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
--- two different
2) The next one occurs, between:
two possible directions again.
This makes that the path taken
from the origin was among:
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 /
=> 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,
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
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:
When the type of economy changes (new leading
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
It occurs usually as a chain of upwards or downward steps,
or sometimes through a major percolation (see that word).
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
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