Lorentz Attractor

Trajectory resulting from integrating the lorentz attractor equations.

The Lorentz Attractor is a simple set of three coupled nonlinear ODEs.

$var element = document.getElementById("moose-equation-3f0abf14-6f98-484a-9790-b54ee6fee802");katex.render("\\begin{aligned} \\frac{dx}{dt} &= \\sigma (y - x) \\\\ \\frac{dy}{dt} &= x(p - z) - y \\\\ \\frac{dz}{dt} &= xy - R z \\end{aligned}", element, {displayMode:true,throwOnError:false});$

In this simulation, the parameters $var element = document.getElementById("moose-equation-56ba2663-e817-4401-b49e-52fb3973d80f");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ , p, and R are given values 10, 28, and 8/3, respectively. The [ChemicalReactions] block of the input file is shown below. They are added with brackets to denote that they are parsed functions; this allows the user to easily change the parameters from the input file. This system of "reactions" is equivalent to the system of ODEs.



[ChemicalReactions]
  [./ScalarNetwork]
    species = 'x y z'
    equation_constants = 'sigma R p'
    equation_values = '10.0 8.0/3.0 28.0'

    reactions = 'x -> a                : {sigma}
                 y -> x + y            : {sigma}
                 x -> x + y            : {p}
                 y -> a                : 1.0
                 x + z -> x + y + z    : -1.0
                 x + y -> x + y + z    : 1.0
                 z -> a                : {R}'
  [../]
[]