General information about Henon model

The set of equations that we are now going to study was proposed by the French astronomer Michel Henon (1976) and can be presented as a simplified model of the Poincare map for the Lorenz model.

Here is the bi-dimentionnal application :

As will be seen in the theoritical study, the parameter b is a measure of the rate of area contraction (dissipation).

Bounded solutions exist over a range of a and b values, and a portion of this range (about 6%) yields chaotic solutions as shown below :

NB: This image was taken from the internet, so notice that a=-a and b=b.

The usual values used to produce chaotic solutions are a = 1.4, b = 0.3. Initial conditions of x = 0, y = 0 will enable you to draw the strange attractor of Henon model.

Here is the result of 10 000 iterations with the fortran code provided.

After this brief presentation, I suggest you should have a look at the theoritical study, however, you can still go back to the main page.