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In the mathematics of dynamical systems, the double-scroll attractor (sometimes known as Chua's attractor) is a strange attractor observed from a physical electronic chaotic circuit (generally, Chua's circuit) with a single nonlinear resistor (see Chua's Diode). The double-scroll system is often described by a system of three nonlinear ordinary differential equations and a 3-segment piecewise-linear equation (see Chua's equations). This makes the system easily simulated numerically and easily manifested physically due to Chua's circuits' simple design. Using a Chua's circuit, this shape is viewed on an oscilloscope using the X, Y, and Z output signals of the circuit. This chaotic attractor is known as the double scroll because of its shape in three-dimensional space, which is similar to two saturn-like rings connected by swirling lines. The attractor was first observed in simulations, then realized physically after Leon Chua invented the autonomous chaotic circuit which became known as Chua's circuit. The double-scroll attractor from the Chua circuit was rigorously proven to be chaotic through a number of Poincaré return maps of the attractor explicitly derived by way of compositions of the eigenvectors of the 3-dimensional state space. Numerical analysis of the double-scroll attractor has shown that its geometrical structure is made up of an infinite number of fractal-like layers. Each cross section appears to be a fractal at all scales. Recently, there has also been reported the discovery of hidden attractors within the double scroll. In 1999 Guanrong Chen (陈关荣) and Ueta proprosed another double scroll chaotic attractor.〔Chen G., Ueta T. Yet another chaotic attractor. Journal of Bifurcation and Chaos, 1999 9:1465.〕 Chen system: Plots of Chen attractor can be obtained with Runge-Kutta method：〔阎振亚著 《复杂非线性波的构造性理论及其应用》第17页 SCIENCEP 2007年〕 parameters:a = 40, c = 28, b = 3 initial conditions:x(0) = -0.1, y(0) = 0.5, z(0) = -0.6 ==Multiscroll attractors== Multiscroll attractors also called ''n''-scroll attractor include the Lu Chen attractor,the modified Chen chaotic attractor, PWL Duffing attractor, Rabinovich Fabrikant attractor,modified Chua chaotic attractor, that is, multiple scrolls in a single attractor. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multiscroll attractor」の詳細全文を読む スポンサード リンク
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