Lorenz Attractor

This is a model of a nonlinear feedback system in continuous-time:

This nonlinear feedback system is the well-known Lorenz attractor, which exhibits chaotic behavior in the form of an unstable periodic orbit. The system is given by the differential equations:

    dx1/dt = sigma*(x2-x1)
    dx2/dt = (lambda-x3)*x1 -x2
    dx3/dt = x1*x2-b*x3

The applet above simulates these differential equations using the CT (continuous-time) domain in Ptolemy II. The CT domain includes a sophisticated numerical solver for differential equations. The plot shows x2 vs. x1. The initial conditions of the states are all 1.0. The parameters sigma, lambda and b can be modified to change the behavior of the model.

Above, the applet has been implemented directly in Java (see the source code). An alternative definition uses the Ptolemy II schematic editor called Vergil.

See Fishwick, Simulation Model Design and Execution: Building Digital Worlds, Prentice Hall, 1995, pp213-214.