Sprott. Some simple chaotic flows

Sprott's simple chaotic flows are a set of three-dimensional differential equations that exhibit chaotic behavior. They were discovered by Professor James Sprott of the Department of Physics at the University of Wisconsin-Madison.

The equations have the form:

dx/dt = a(y - x)
dy/dt = xz - by
dz/dt = xy - cz

where a, b, and c are constants. These equations can produce a wide variety of chaotic behavior, including strange attractors, limit cycles, and periodic orbits.

Sprott has identified several different types of flows, each with distinct behavior. Some examples include the Lorenz-like attractor, the double-scroll attractor, and the symmetric butterfly attractor.

The Sprott flows are important in the study of chaos theory and nonlinear dynamics, and have practical applications in fields such as physics, engineering, and computer science. They are also used as test cases for numerical methods and algorithms designed to simulate chaotic systems.