Tridimensional visualization of the Verhulst dynamics [Visualisation tridimensionnelle de la dynamique de Verhulst].

The Verhulst dynamics is defined using the following iteration:
```                    X  = 0.5
0
```
```                    X  = RX   (1 - X   )
n     n-1      n-1
```
Here, in this computation, the growing rate 'R' is no longer constant but changes its value periodically using the following arbitrary cycle:
```R3 ==> R3 ==> R3 ==> R3 ==> R2 ==> R2 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R2 ==> R2 ==> R3 ==> R3 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R2 ==> R2 ==> R3 ==> R3 ==> R2 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R1 ==> R1
```
(based on the sine function on [0,8.pi]) where {R1,R2,R3} are respectively the three coordinates of the current point inside the following domain [2.936,3.413]x[3.500,3.850]x[3.000,4.000]. Only the points corresponding to a dynamical system with a negative Lyapunov exponent are displayed.

See a close-up:

See a bidimensionnal dynamics:

(CMAP28 WWW site: this page was created on 12/03/2010 and last updated on 08/14/2021 11:27:51 -CEST-)

[See the generator of this picture [Voir le générateur de cette image]]

[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]

[See the following comment(s): Verhulst dynamics [Voir le(s) commentaire(s) suivant(s): dynamique de Verhulst]]

[Go back to AVirtualMachineForExploringSpaceTimeAndBeyond [Retour à AVirtualMachineForExploringSpaceTimeAndBeyond]]

[The Y2K Bug [Le bug de l'an 2000]]

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]