Multiscroll attractor
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The double scroll 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.
This chaotic attractor is known as the double scroll because of its shape in the three-dimensional space. Using a Chua's circuit, this shape is viewed on an oscilloscope using the X, Y, and Z output signals of the circuit.
The attractor was first observed in simulations, then realized physically after Leon Chua invented the autonomous Chua's circuit.[1] The double scroll attractor from the Chua circuit was proven to be chaotic through a number of Poincaré return maps associated with the attractor which can be derived explicitly in analytical form via compositions of eigenvectors within each linear region of the 3-dimensional state space.[2]
Numerical analysis of the double scroll attractor has shown that its geometrical structures is made up of and infinite number of concentric, oppositely-directed, fractal-like layers. The local geometry of each cross section appears to be a fractal at all cross sections and scales.[3] Recently, there has also been reported the discovery of hidden attractors within the double scroll.
Variations on the double scroll comprise the family of so-called n-scrolls, that is, from 1 to 9 scrolls in a single attractor.
See Also
References
- ^ Matsumoto, Takashi (December 1984). "A Chaotic Attractor from Chua's Circuit" (PDF). IEEE Transactions on Circuits and Systems. CAS-31 (12). IEEE: 1055–1058.
- ^ Chua, Leon. "Chua circuits". Scholarpedia.
- ^ Chua, Leon. "Fractal Geometry of the Double Scroll Attractor". Scholarpedia.