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]}

Chen attractor

The Chen system is defined as follows^{[7]}

${\frac {dx(t)}{dt))=a(y(t)-x(t))$

${\frac {dy(t)}{dt))=(c-a)x(t)-x(t)z(t)+cy(t)$

${\frac {dz(t)}{dt))=x(t)y(t)-bz(t)$

Plots of Chen attractor can be obtained with the Runge-Kutta method:^{[8]}

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]}