# 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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By selecting different control parameter, the chaotic motion of the system can be suppressed to different periodic orbits.
Zhang, "Multi-pulse chaotic motions of high-dimension nonlinear system for a laminated composite piezoelectric rectangular plate," Meccanica, vol.
The Runge-Kutta method is utilized to investigate the bifurcations and chaotic motions of cracked plate.
19(a)-(d) show spreading, no clear indication appears about nature of chaotic motion and three-dimensional spreading of the particle path for the cases pointed out above.
Chaotic motion produced by resonant forcing is discussed later in the chapter.
For example, chapter 2 explains the notion of fractal intricacy, chapter 6 takes up the "universal" patterns by which systems can go from nonchaotic to chaotic motion upon parameter variation, chapter 9 explores the senses in which chaotic motion can be associated with randomness (in the "product" sense) of the dynamical orbits, and chapter 10, directed at the problem of giving a formal definition of a chaotic system, delves more deeply into the basic mathematical structures that lie behind the chaotic results.
All the necessary ingredients for chaotic motion are present in the equations.
The developed theory is linked to fractals in the sense of Mandelbrot (1983) because truly chaotic motion often possesses the intricate geometry of the fractal.
The shelves of his office are filled with toys, which he coaxes into chaotic motion for the entertainment of visitors.
They cover the qualitative analysis of motion in a three-body system, motions of small bodies in the planetary system, the chaotic motion of orbits, and orbit diffusion.
Nevertheless, a deeper understanding of the bifurcation evolution as well as the transition between stable periodic and chaotic motion is still essential for designing and adjusting the key parameters to enable the system to perform well.
This talk will present a simplified two dimensional animated model of Hyperion's more complicated full three dimensional motion which, although not capable of showing chaotic motion (three dimensions are required for chaos in a physical system) does show how a driving torque of Saturn's tidal force functions.

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