New class of chaotic systems with circular equilibrium | SpringerLinkChaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaos theory is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems , there are underlying patterns, constant feedback loops , repetition, self-similarity , fractals , and self-organization. The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state, meaning there is sensitive dependence on initial conditions. A metaphor for this behavior is that a butterfly flapping its wings in China can cause a hurricane in Texas. Small differences in initial conditions, such as those due to rounding errors in numerical computation, yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.
Lecture - 28 Analysis of Chaotic Time Series
Chaos and Time-Series Analysis
Becker, D. Burkle, R. Happe, and others. Springer, Schreiber, Thomas.
Chaos and Time-Series Analysis. J. C. Sprott A web page supplement to the book by the above title. Book Cover. This page contains supplementary materials .
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Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems. Chaotic maps often generate fractals. Although a fractal may be constructed by an iterative procedure, some fractals are studied in and of themselves, as sets rather than in terms of the map that generates them. This is often because there are several different iterative procedures to generate the same fractal.