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The nature of chaos theory suggests that the predictability of any system is limited because it is impossible to know all of the minutiae of a system at the present time. In principle, the deterministic systems that chaos theory attempts to analyze can be predicted, but uncertainty in a forecast increases exponentially with elapsed time. [2]
Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [2]
The idea demonstrates that there are occurrences where theory's predictions are effectively not possible. Wolfram states several phenomena are normally computationally irreducible [citation needed]. Computational irreducibility explains why many natural systems are hard to predict or simulate.
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz.
The easy experimental implementation of the circuit, combined with the existence of a simple and accurate theoretical model, makes Chua's circuit a useful system to study many fundamental and applied issues of chaos theory. Because of this, it has been object of much study and appears widely referenced in the literature.
In mathematics, a chaos machine is a class of algorithms constructed on the base of chaos theory (mainly deterministic chaos) to produce pseudo-random oracles.It represents the idea of creating a universal scheme with modular design and customizable parameters, which can be applied wherever randomness and sensitiveness is needed.
Experimental control of chaos by one or both of these methods has been achieved in a variety of systems, including turbulent fluids, oscillating chemical reactions, magneto-mechanical oscillators and cardiac tissues. [6] attempt the control of chaotic bubbling with the OGY method and using electrostatic potential as the primary control variable.
Whereas the (global) Lyapunov exponent gives a measure for the total predictability of a system, it is sometimes of interest to estimate the local predictability around a point x 0 in phase space. This may be done through the eigenvalues of the Jacobian matrix J 0 ( x 0 ) .