Chaos Theory is a branch of mathematics that touches on many other large fields of study, such as economics, ecology and natural sciences.
It has countless applications in such disciplines too. The theory and its investigation can be summed up with the collection of systems which are extremely sensitive to the original conditions and the conditions about which they take place. Such erratic behaviour is often called the Butterfly Effect, in which it has been speculated that the flapping of a butterfly’s wings in the Amazonian rainforest can eventually grow in size to become a tornado in Texas.
It is believed that the erratic and unpredictable nature of such systems is due to the inevitable rounding off that takes place when multi-step operations are monitored or predicted. In this respect, it is related to iteration equations. Chaotic behaviour makes predicting results in the distat future almost impossible in some mathematical models. This is in spite of the deterministic nature of such systems, coupled with the lack of random influences.
It is chaos that makes forecasting the weather such a foreboding task. There are several approaches in order to attempt to remedy this. One such method is by recurrence formulae, and in the example of weather forecasting, microclimate modelling. Long term trends in the past thirty years are analysed.
Chaos Theory touches on computer programming, political science and on philosophy. Knowledge about this aspect of the natural world is therefore essential for students of many different academic disciplines. It is also possible to observe chaos in laboratory settings in various chemical reactions (particularly oscillating ones like the clock reaction and the BZ reaction), magnetic systems and in electronic circuitry. Variations in the orbital behaviour of natural satellites can also be analysed with an understanding of chaos theory. Population changes of certain species, especially with variations of predators and prey, can also exhibit chaotic behaviour. Chaos also takes place on a sub-atomic level.
When applied to ecological and population growth/decay models, it is often called a Ricker Model. It is believed by some neurologists that epileptic seizures can be predicted by considering the chaotic nature of the condition. Research is ongoing in this field of investigation. Chaotic systems which obey general relativity theory are called relativistic chaotic systems.
Chaos in everyday language implies a sense of disorder. There is a more discrete meaning when used technically, however. The precise definition is a matter of some debate. Collectively, chaotic systems have a profound sensitivity to initial conditions, have high density periodic orbits and exhibit topological mixing. It is the high sensitivity to initial values which is the basis behind the lack of any periodicity and cyclic nature of the system and the absence of any convergence.
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