# chaos theory

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## chaos theory

a branch of mathematics that seeks to predict widespread effects of small (or minute) and possibly remote triggering events; the unpredictable course of some epidemics and malignant metastases may accord with chaos theory.

## chaos theory

The mathematical conception that some phenomena that seem random may be of a deterministic order highly sensitive to initial conditions and perturbations. There is a growing appreciation that chaos may be a feature of many biological systems and that chaos theory may prove to have many applications in medicine.
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Numerical simulation indicates that the system performs complex dynamic behaviors, such as multiperiodic motion and chaotic motion, when [[OMEGA].sub.1] changes in a certain region.
The existence of irregular chaotic motion in nonintegrable systems was pointed out.
Dynamic behaviors can be more clearly observed over a range of parameter values in bifurcation diagrams, which are widely used to describe transitions from periodic motion to chaotic motion in dynamic systems.
The dynamic behaviors of system in (1) appear as the switch of periodic and chaotic motions with the variable [l.sub.1] varying.
With the bifurcation parameter [epsilon] increasing, as [epsilon] = 1.40, the gear system will be from periodic 2 motion to chaotic motion. Taken [epsilon] = 1.42, the Poincare map of the system is shown in Fig.
The main purpose of the present study is to investigate the chaotic motion of the nonlinear differential equation shown in (1) by evaluating the critical value of the forcing amplitude given in (9).
Chaotic motion of nonlinear systems can generate attractors in the phase space with unique nature.
A spectrum called Lyapunov exponents (LE) is often used as a quantifier  of chaotic motion or regular motion.
Sharma said that the interesting puzzle has always been how to predict the seemingly chaotic motion of a turbulent fluid.
The above are repeated for many values of the wave amplitude, over and under the threshold to chaos, in order to examine the radiation behavior during the transition from ordered to chaotic motion.
Therefore the domestic and foreign researchers put the traditional control theory and chaotic motion characteristics used in chaos control and present a lot of chaos control method, such as delayed feedback control [4, 5], periodic parameter perturbation control , continuous feedback control , pulse feedback control , and adaptive control , and so forth.
One-dimensional noninvertible maps are the simplest systems with capability of generating chaotic motion (Ott, 2002).

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