The Chaos Theory or the Science of Complexity presents an interesting perspective from the viewpoint of their application to the economy especially in explaining phenomena that seem to have a disruptive behavior. Behind the apparent disorder in the economy, there is a dynamic that can be explained through mathematical techniques and appropriate, typical statistics of this theory. In dynamic systems such as the economy, constantly changing over time, small changes at a given time, may be the cause of great importance in the future.

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CHAOS OR COMPLEXITY IN ECONOMIC SYSTEMS
Fernando Alcoforado *
Backed by the physics laws of Newton described by differential equations, scientists
believed for a long time that nature is deterministic knowing based on them that it was
possible to predict all phenomena. Around the turn of the nineteenth to the twentieth
century, advances in the natural sciences and mathematics have expressed serious
doubts about the validity of the mechanistic Newtonian view. The theory of relativity
and quantum mechanics challenged the deterministic world view. Quantum mechanics
introduced the uncertainty principle. The Chaos Theory or Complexity Science
represented one of the major breakthroughs in scientific research of the twentieth
century ending with the dichotomy that existed in the traditional deterministic approach
between determinism and randomness.
In the traditional deterministic approach, the uncertainty was seen as a result of
ignorance of the different causes involved in the realization of an event as well as the
complexity of it. In 1908, the French mathematician Henri Poincaré (1854-1912), who
had studied the nonlinear mathematical systems reached conclusions which, over time,
would be important to conceptualize the Chaos Theory. Poincaré said that, if we know
exactly the natural laws that govern the evolution of the Universe, we can predict
exactly your situation at any given moment of time, but as we never know exactly the
initial state of the Universe we would always be making a mistake to define it. In other
words, the initial state of the Universe can be known only with some approximation.
Even assuming that we could determine the laws governing their evolution, our
prediction of any subsequent state would also be approximate.
Until then approach the predictions would not be attributable to the existence of chaos
in reality, but a limitation in our knowledge of the initial conditions. Henri Poincaré
realized his pioneering studies in this field concluding that complex systems are not
required to produce randomness. Poincaré studies are updated in the 1960s thanks to
mathematician and American meteorologist Edward Lorenz. His perplexity had much to
do with the inability to predict climatic events beyond a certain number of days. In the
early 1960s, Lorenz began to develop a mathematical model to predict atmospheric
phenomena, and by chance he discovered that the same mathematical tool used
produced unexpected and unpredictable differences in outcome when simulated small
changes in initial conditions.
Efforts of Poincare and Lorenz were added to the contributions of Benoit Mandelbrot
(communications engineer), Edward Feigenbaum (math), Libchaber (physical), Winfree
(biologist), Mandell (psychiatrist) and others. Chaos Theory or the new Science of
Complexity suggests that the world should not strictly follow the deterministic
Newtonian model, predictable and certain, because it has chaotic aspects. The observer
is not who creates instability or unpredictability due to their ignorance because they
exist in nature. A typical example is the weather. The processes of reality depend on a
huge set of uncertain circumstances that determine, for example, that any small change
in one part of the planet, there will be in the coming days or weeks a considerable effect
on the other part of the Earth. This condition also applies to the economic system.
According to Chaos Theory or Complexity Science, chaos is a "mixture" of disorder and
order that born of new structures, structures called "dissipative". Chaos theory suggests
that the Universe has a cycle of order, disorder, order, and so on. So that one leads the

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other and so on, perhaps indefinitely. One of the main implications of Chaos Theory has
to do with the return generated in chaotic situations. While closed systems have a
negative feedback, open systems evolve chaotically by positive feedback (Figure 1).
Negative feedback tends to correct a deviation, leading the system to its original state.
An imbalance is a deviation that is corrected by a return to the initial equilibrium. Such
processes oppose change, since always look back to return to a previous state. On the
other hand, positive feedback promotes change, the formation of new structures, more
sophisticated, more adaptable, and more subtle. Insofar as it entails the creation of a
new structure, the processes are irreversible, unlike negative feedback, which tends to
the original state and is reversible.
Figure 1 - Systems theory
Deviations neutralize the negative feedback and amplify the positive feedback. To
illustrate, if we walk in the desert towards a distant goal, we must, from time to time,
correct our course, neutralizing our deviation from the target through regular updates on
our way. But if we make a mistake of a millimeter of the target, with time the error will
be magnified more and eventually arrive at a place far from the goal. In the negative
feedback we seek to correct the deviations to return to the original path. In positive
feedback, small changes can lead to big changes that lead to new targets unknown,
perhaps better, although we cannot predict exactly where it will arrive.
While classical science focused on stability, on determinism, emphasizes the process of
negative feedback which tends to reduce the change, returning the system to its
equilibrium position, the positive feedback promotes change and instability. Example:
technological innovation creates a new business and the presence of this, in turn,
stimulates the generation of more innovations. Positive feedback means that when one
variable increases, so does the other (or when one decreases, so does the other). This
explains how small change creates great end change (butterfly effect).
Evolution requires that instability for small events are magnified fact that is only
possible in a situation of imbalance. Evolution requires instability, irreversibility and the
possibility of making sense of small events so that a structural change occurs. The
irreversibility makes possible impossible things in a state of balance and provides an
important constructive law, the origin of a new state and its structures highly complex
and sophisticated as the market or society.
Once the process results in the creation of a complex structure, the dissipation structure,
a new cycle of imbalance occurs and chaos starts where new imbalance or fluctuations
occur (Figure 2). For Prigogine (Russian chemist, Nobel Prize in Chemistry 1977 for his

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work in thermodynamics of irreversible processes with the formulation of the theory of
dissipative structures), all systems contain subsystems constantly fluctuating.
Sometimes, a single change in one of them can be as powerful as a result of a positive
feedback, which breaks all the existing organization. At that moment, called singular
moment or bifurcation point, is inherently impossible to know where the system will
evolve (state of improbability) disintegrate into chaos or jump to a new level of superior
organization and differential ie, a new dissipative structure.
Figure 2 - Dynamic Systems
Source: Ervin Laszlo. O Ponto do Caos (The Chaos Point). São Paulo: Editora Cultrix, 200.
Figure 2 shows what happens to a dynamic system such as the economic system of a
country when it is subject to "fluctuations" that leads to a bifurcation point from which
the system reaches a new dynamic stability (breakthrough) or enter collapse, according
to Ervin Laszlo (the Chaos Point São Paulo: Publisher Cultrix, 200). Figure 2 shows
that at the bifurcation point the system has to be restructured or collapse. This is the
situation faced by many countries, including Brazil, which, after the crisis that erupted
in 2008 in the United States and spilled over the planet, did not object to restructure its
economic system by the Brazilian government.
It is worth noting that chaos is present in a wide variety of disciplines of science.
Research on the chaos began in the 1970s physiologists when began to investigate why
the chaos of normal heartbeats produced a sudden cardiac arrest, ecologists analyzed
how certain places on the planet have experienced random changes in nature, engineers
sought to discover the causes of behavior to erratic oscillators, chemists analyzed the
causes of unexpected fluctuations in the reactions of chemicals and economists tried to
detect some kind of order in unexpected changes in prices, etc. In classical science,
chance was an intruder, but Chaos Theory has become a partner of determinism.
The Chaos Theory or the Science of Complexity presents an interesting perspective
from the viewpoint of their application to the economy especially in explaining
phenomena that seem to have a disruptive behavior. Behind the apparent disorder in the
economy, there is a dynamic that can be explained through mathematical techniques and
appropriate, typical statistics of this theory. In dynamic systems such as the economy,
constantly changing over time, small changes at a given time, may be the cause of great
importance in the future. The global crisis that erupted in 2008 in the United States

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produced several consequences that manifest themselves today. Considering that the
capitalist economy is a dynamic, non-linear and complex system, the difficulty to plan
and anticipate problems, requires consideration of the prospects for long-term
development. Means you have to plan the economy recognizing that chaos and
complexity are present and that must deal with this scenario the best way possible.
*Fernando Alcoforado , member of the Bahia Academy of Education, engineer and doctor of Territorial
Planning and Regional Development from the University of Barcelona, a university professor and
consultant in strategic planning, business planning, regional planning and planning of energy systems, is
the author of Globalização (Editora Nobel, São Paulo, 1997), De Collor a FHC- O Brasil e a Nova
(Des)ordem Mundial (Editora Nobel, São Paulo, 1998), Um Projeto para o Brasil (Editora Nobel, São
Paulo, 2000), Os condicionantes do desenvolvimento do Estado da Bahia (Tese de doutorado.
Universidade de Barcelona, http://www.tesisenred.net/handle/10803/1944, 2003), Globalização e
Desenvolvimento (Editora Nobel, São Paulo, 2006), Bahia- Desenvolvimento do Século XVI ao Século XX
e Objetivos Estratégicos na Era Contemporânea (EGBA, Salvador, 2008), The Necessary Conditions of
the Economic and Social Development-The Case of the State of Bahia (VDM Verlag Dr. Muller
Aktiengesellschaft & Co. KG, Saarbrücken, Germany, 2010), Aquecimento Global e Catástrofe
Planetária (P&A Gráfica e Editora, Salvador, 2010), Amazônia Sustentável- Para o progresso do Brasil e
combate ao aquecimento global (Viena- Editora e Gráfica, Santa Cruz do Rio Pardo, São Paulo, 2011)
and Os Fatores Condicionantes do Desenvolvimento Econômico e Social (Editora CRV, Curitiba, 2012),
among others.