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Lorenz Model

Model Type
SES Library XPP model

This simple model was developed by Edward Lorenz in 1963 to study fluid mechanics (based on Navier-Stokes equations). It is the first ever model of a chaotic dynamical system. Chaos arises when a deterministic, nonlinear dynamical system exhibits long-term unpredictability in behavior due to sensitivity to initial conditions.

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.  When plotted in the three spatial dimensions, the dynamics of the model describe a shape called \"strange attractor.\"

Default Dynamics

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Lorenz

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No state variables defined.

Name Default Value Description
$\sigma$ - Convection parameter
\(r\) - -
\(b\) - -
\(c\) - -
\(del\) - -
$$\frac{dx}{dt} = \sigma (y - x)$$
$$\frac{dy}{dt} = x (\rho - z) - y$$
$$\frac{dz}{dt} = xy - \beta z$$
lorenz_model.ode
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Download Source File (lorenz_model.ode)

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

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