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Animated demonstration of the Lorenz Model

Model Type
SES Library XPP model

Animated demonstration of the Lorenz model and its sensitivity to initial conditions.  The simulation starts with twenty points very close to each other, and follows them as they move further away. The starting values differ in the fifth and sixth significant digits of a single coordinate.

The Lorenz model was developed by Edward Lorenz in 1963 to study fluid mechanics.The model is a three-dimentional system of differential equations. Specifically, the model describes the convection motion of a fluid in a small idealized \"Rayleigh-Benard\" container. The basic presumption is that there is fluid in a container with surfaces at different temperatures. The model shows that the fluid motion eventually leads to a chaotic behavior.

Reference

Lecture notes by David Marshall (Professor at University of Oxford). Link: http://www.atm.ox.ac.uk/user/marshall/ffc/lecture13.pdf

Default Dynamics
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Lorenz 20
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Download Animation File (lorenz_20.ani)

No state variables defined.

No parameters defined.

$$\frac{dx}{dt} = \sigma (y - x)$$
$$\frac{dy}{dt} = x (\rho - z) - y$$
$$\frac{dz}{dt} = xy - \beta z$$
animated_demonstration_of_the_lorenz_model.ode
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Download Source File (animated_demonstration_of_the_lorenz_model.ode)

The source code file can be used with XPP/XPPAUT or other simulation tools.

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