transition to chaos

transition to chaos

[tran′zish·ən tə ′kā‚äs]
(physics)
The process by which a system evolves from periodic toward chaotic behavior as one or more parameters governing the behavior of the system are varied.
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In the Transition to Chaos [6], a system evolves toward non periodic time dependence as one or more parameters are varied.
For this reason the study of the transition to chaos must be made with computers.
Seeing that dealing with non-linear systems is not straightforward at all, determining the parameters that generate the transition to chaos for a given differential equation is not an easy undertaking, and one way of detecting them may be by trialand-error.
In order to investigate the transition to chaos in the Non-Linear Damped and Forced Oscillator, its mathematical model must be constructed.
In the Transition to Chaos [10], a system evolves toward non periodic time dependence as one or more parameters are varied.
In view of the fact that the system under investigation is subject to dissipation (damping b) and since there are two competing frequencies, it is expected to observe a transition to chaos [1].
Based on both experience and physical intuition the set of parameters where the oscillator under study shows a transition to chaos was successfully determined with the help of the developed software and after just a few trials, the result is shown in fig.
The creation of a Virtual Lab to investigate the transition to chaos in second order non-linear differential equations has been reported.
Now researchers have turned up theoretical and experimental evidence suggesting that this phase transition from an ordered to a disordered state may be an example of a transition to chaos.
While studying the transition to chaos in the damped non-linear forced oscillator, this author observed that its route to chaos resembles the steps followed by a machine when it is on the verge of collapsing, and that chaos, this is the absence of a frequency, when the period becomes infinite (1-3), may be paralleled to machine collapse.
In the next section the equation used by this author in the computer simulation of the transition to chaos is deduced, this may be found in any General Physics book used by university students of Physics and Engineering.
2 very clearly displays the transition to chaos through a cascade of frequency bifurcations; a characteristic route taken by many systems evolving towards chaos (2).

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