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The Hénon Map

A Hénon map is a discrete-time dynamical system described by the following equations:

$\begin{aligned} x_{t+1} &= 1 - ax_t^2 + y_t \\ y_{t+1} &= bx_t \end{aligned}$

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

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

class Hénon(a: Double, b: Double) extends DiscreteProcess("Henon") {
  val x = Double("ex:x")
  val y = Double("ex:y")
  n(x) := 1.0 - a * x*x + y
  n(y) := b * x
}

class HénonModel extends Model {
  val a = Double("ex:a") := 1.4
  val b = Double("ex:b") := 0.3
  def process = new Hénon(a, b)
}

The $n(x)$ operator denotes the value of $x$ at the next time, that is at $t+1$.

Running the model for 25000 time steps and graphing the output produces:

graphic of Henon map