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The Rössler Attractor

A Rössler attractor is generated by the following system of differential equations:

$\begin{aligned} \frac{dx}{dt} &= -y - z \\ \frac{dy}{dt} &= x + ay \\ \frac{dz}{dt} &= b + z(x - c) \\ \end{aligned}$

It is a simple example of the use of the ODE class and is implemented in the Roessler.scala file as follows just like this:

import uk.ac.ed.inf.mois.Model
import uk.ac.ed.inf.mois.ODE

class Roessler(a: Double, b: Double, c: Double) extends ODE("Roessler") {
  val x = Double("ex:x")
  val y = Double("ex:y")
  val z = Double("ex:z")
  d(x) := -y - z
  d(y) := x + a*y
  d(z) := b + z * (x - c)
}

class RoesslerModel extends Model {
  val Double("ex:a") := 0.2
  val Double("ex:b") := 0.2
  val Double("ex:c") := 5.7
  val process = new Roessler(a, b, c)
}

The $d(x)$ operator, which may also be written as $d(x)/dt$ denotes the time derivative of $x$ with respect to $t$ as might be supposed.

Running the model for 1000 time steps and graphing the output with gnuplot produces:

Roessler attractor