Singularity and Chaos Theory
In this chapter we will deal with the notions of both singularity and chaos. These are two of the major notions to study, evaluate and proactively address the risk at the right time based on proper prediction. In our dynamic complexity mathematical emulat
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Singularity and Chaos Theory
Chaos is inherent in all compounded things. Strive on with diligence. —Buddha
Introduction In this chapter we will deal with the notions of both singularity and chaos. These are two of the major notions to study, evaluate and proactively address the risk at the right time based on proper prediction. It may happen that small differences in the initial positions may lead to enormous differences in the final phenomena. Prediction becomes impossible.
This is the statement, which gives Poincare the claim to the title ‘‘Father of Chaos Theory.’’ This is the first known published statement of the property now known as ‘‘sensitivity to initial conditions’’, which is one of the defining properties of a chaotic dynamical system.
Why Singularity and Chaos Point Is Important to Discover and Predict In our dynamic complexity mathematical emulation research we discovered that a sudden increase in dynamic complexity could dramatically impact the system productivity, the service quality or the cost of operations. At a certain point the degradation becomes visible and sometimes risky due to the fact that the system starts to produce less and costs more up to a point where the degradation rate becomes too fast that little change in initial conditions can produce a ‘‘singularity.’’ At such point the solution may produce peculiar results or even show no solution at all. At this point or near to it, chaos (simply a point of non-return) may be produced Springer-Verlag Berlin Heidelberg 2014 N. Abu el Ata and M.J. Perks, Solving the Dynamic Complexity Dilemma, DOI 10.1007/978-3-642-54310-4_17
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Singularity and Chaos Theory
accompanied by the inability to get back to normal conditions (examples of a chaos are the 2008 Economic Meltdown, Fukushima Daiichi nuclear disaster, Deepwater BP oil spill, etc.). As we have said before, asking the butterfly in China to flap its wings backwards will not reverse the avalanche in the Alps. However we observed a number of situations where multiple singularities may take place and these are commonly considered as mini-crisis or a symptom that will end by provoking a major singularity leading to a spectacular chaos. This we can call the approaching-crisis or the prelude-period when many believe that a crisis is due but do not know when it is due. Often optimistic positions (a.k.a. inactivity) are taken.
The Chaos Theory As we mentioned earlier the great French mathematician Henri Poincaré (1854–1912) is the legitimate father of Chaos Theory. While Isaac Newton gave the world the principles of how the solar system works, Poincare pointed out that Newton’s 3-body solution was insufficient to explain the system. The reason is that Newton’s differential equations are limited to the expression of the interaction between 2 bodies at a time. A attracts B. B attracts C. But A doesn’t attract B and C at the same time according to the mathematics. This is really one of the science’s anarchies: what will happen if 3 or more bodies are allowed in the in the model? In
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