Strange attractor connected by two 2-dimensional rings
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.[1] The double-scroll attractor from the Chua circuit was rigorously proven to be chaotic[2] 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.[3]
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.[4] Recently, there has also been reported the discovery of
hidden attractors within the double scroll.[5]
In 1999
Guanrong Chen (陈关荣) and Ueta proposed another double scroll chaotic attractor, called the Chen system or Chen attractor.[6][7]
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.[9]
Lu Chen attractor
An extended Chen system with multiscroll was proposed by Jinhu Lu (吕金虎) and Guanrong Chen[9]