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List Of Chaotic Maps
In mathematics, a chaotic map is a map (mathematics), map (an Discrete-time dynamical system, evolution function) that exhibits some sort of chaotic behavior. 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 and Iterated function, iterated functions often generate fractals. Some fractals are studied as objects themselves, as set (mathematics), sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems). List of chaotic maps List of fractals * Cantor set * de Rham curve * Gravity set, or Mitchell-Green gravity set * Julia set - derived from complex quadratic map * Koch snowflake - special case of de Rham curve * Lyapunov fractal * Mandelbrot set - derived from complex quadratic ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chua Circuit
Chua's circuit (also known as a Chua circuit) is a simple electronic circuit that exhibits classic chaos theory, chaotic behavior. This means roughly that it is a "nonperiodic oscillator"; it produces an oscillating waveform that, unlike an ordinary electronic oscillator, never "repeats". It was invented in 1983 by Leon O. Chua, who was a visitor at Waseda University in Japan at that time. The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system, leading some to declare it "a paradigm for chaos". Chaotic criteria An autonomous circuit made from standard components (resistors, capacitors, inductors) must satisfy three criteria before it can display chaotic behaviour. It must contain: # one or more nonlinear elements, # one or more locally active resistors, # three or more energy-storage elements. Chua's circuit is the simplest electronic circuit meeting these criteria. As shown in the top figure, the energy storage elements are two ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chen Chaotic Attractor
Chen or Ch'en may refer to: People *Chen (surname) (陳 / 陈), a common Chinese surname *Chen (singer) (born 1992), member of the South Korean-Chinese boy band EXO * Chen Chen (poet) (born 1989), Chinese-American poet * (), a Hebrew first name or surname: ** Hen Lippin (born 1965), former Israeli basketball player ** Chen Kugel (born 1962), Israeli pathologist who did an autopsy on Yahya Sinwar ** Chen Reiss (born 1979), Israeli operatic soprano ** Ronen Chen (born 1965), Israeli fashion designer Historical states *Chen (state) (c. 1045 BC–479 BC), a Zhou dynasty state in present-day Anhui and Henan *Chen (Thessaly), a city-state in ancient Thessaly, Greece * Chen Commandery, a commandery in China from Han dynasty to Sui dynasty *Chen dynasty (557–589), a Chinese southern dynasty during the Northern and Southern dynasties period Businesses and organizations * Council for Higher Education in Newark (CHEN) * Chen (), acronym in Hebrew for the Women's Army Corps (, ) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brusselator
The Brusselator is a theoretical model for a type of autocatalytic reaction. The Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. It is a portmanteau of Brussels and oscillator. It is characterized by the reactions : A \rightarrow X : 2X + Y \rightarrow 3X : B + X \rightarrow Y + D : X \rightarrow E Under conditions where A and B are in vast excess and can thus be modeled at constant concentration, the rate equations become :\left\ = \left\ + \left\^2 \left\ - \left\ \left\ - \left\ \, :\left\ = \left\ \left\ - \left\^2 \left\ \, where, for convenience, the rate constants have been set to 1. The Brusselator has a fixed point at :\left\ = A \, :\left\ = \,. The fixed point becomes unstable when : B>1+A^2 \, leading to an oscillation of the system. Unlike the Lotka–Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bogdanov Map
In dynamical systems theory, the Bogdanov map is a chaotic 2D map related to the Bogdanov–Takens bifurcation. It is given by the transformation: : \begin x_ = x_n + y_\\ y_ = y_n + \epsilon y_n + k x_n (x_n - 1) + \mu x_n y_n \end The Bogdanov map is named after Rifkat Bogdanov. See also * List of chaotic maps References * DK Arrowsmith, CM Place, An introduction to dynamical systems, Cambridge University Press, 1990. * Arrowsmith, D. K.; Cartwright, J. H. E.; Lansbury, A. N.; and Place, C. M. "The Bogdanov Map: Bifurcations, Mode Locking, and Chaos in a Dissipative System." Int. J. Bifurcation Chaos 3, 803–842, 1993. * Bogdanov, R. "Bifurcations of a Limit Cycle for a Family of Vector Fields on the Plane." Selecta Math. Soviet 1, 373–388, 1981. External linksBogdanov mapat MathWorld ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta Chaotic Map
Beta (, ; uppercase , lowercase , or cursive ; or ) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive . In Modern Greek, it represents the voiced bilabial fricative while in borrowed words is instead commonly transcribed as μπ. Letters that arose from beta include the Roman letter and the Cyrillic letters and . Name Like the names of most other Greek letters, the name of beta was adopted from the acrophonic name of the corresponding letter in Phoenician, which was the common Semitic word ('house', compare and ). In Greek, the name was , pronounced in Ancient Greek. It is spelled in modern monotonic orthography and pronounced . History The letter beta was derived from the Phoenician letter beth . The letter Β had the largest number of highly divergent local forms. Besides the standard form (either rounded or pointed, ), there were forms as varied as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
