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Rabinovich–Fabrikant Equations
The Rabinovich–Fabrikant equations are a set of three coupled ordinary differential equations exhibiting Chaos theory, chaotic behaviour for certain values of the parameters. They are named after Mikhail Rabinovich and Anatoly Fabrikant, who described them in 1979. System description The equations are: : \dot = y (z - 1 + x^2) + \gamma x \, : \dot = x (3z + 1 - x^2) + \gamma y \, : \dot = -2z (\alpha + xy), \, where ''α'', ''γ'' are constants that control the evolution of the system. For some values of ''α'' and ''γ'', the system is chaotic, but for others it tends to a stable periodic orbit. Danca and Chen note that the Rabinovich–Fabrikant system is difficult to analyse (due to the presence of quadratic and cubic terms) and that different attractors can be obtained for the same parameters by using different step sizes in the integration, see on the right an example of a solution obtained by two different solvers for the same parameter values and initial conditions. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One Numerical Solution To The Rabinovich-Fabrikant System 01
1 (one, unit, unity) is a number, Numeral (linguistics), numeral, and glyph. It is the first and smallest Positive number, positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit (measurement), unit of counting or measurement, a determiner for singular nouns, and a gender-neutral pronoun. Historically, the representation of 1 evolved from ancient Sumerian and Babylonian symbols to the modern Arabic numeral. In mathematics, 1 is the multiplicative identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a prime number. In Digital electronics, digital technology, 1 represents the "on" state in binary code, the foundation of computing. Philosophically, 1 symbolizes the ultimate reality or source of existence in various traditions. In math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
