LORENZ_EQUATIONS is a collection of Mathematica routines which investigate and display the behavior of solutions to the Lorenz equations.
The Lorenz equations are an extremely simplified model of the weather, in which three differential equations describe the evolution of three variables. There are also three parameters whose values play the role of physical constants.
It was while studying these equations that Edward Lorenz discovered what he called "deterministic chaos". That is, at least for certain values of the parameters, solutions were extremely sensitive to the initial conditions.
The Lorenz equations are often written as
x' = sigma * ( y - x )
y' = x * ( rho - z ) - y
z' = x * y - beta * z
where the parameters are positive. Typical values for the parameters are
sigma = 10
beta = 8 / 3 = 2.666...
rho = 28
The value of rho has a strong influence on the behavior of solutions.
The value rho=28 results in chaotic solutions, whereas rho=99.96 yields
a regular pattern.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
LORENZ_SIMULATION is a MATLAB program which solves the Lorenz equations and displays the solution, for various starting conditions.
Jim Fink, Gettysburg College.
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