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 ==> R2 ==> R2 ==> R2 ==> R1 ==> R1 ==> R1 ==> R2 ==> R3 ==> R2 ==> R1 ==> R1 ==> R1 ==> R3 ==> R3 ==> R1 ==> R1 ==> R1 ==> R2 ==> R3 ==> R2 ==> R1 ==> R1 ==> R1 ==> R2 ==> R2 ==> R2 ==> R3 ==> R3 ==> R3
(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 [3.123,3.327]x[3.700,3.850]x[3.000,3.500]. Only the points corresponding to a dynamical system with a negative Lyapunov exponent are displayed.


See a bidimensionnal dynamics:




(CMAP28 WWW site: this page was created on 11/09/2010 and last updated on 10/11/2024 21:06:58 -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]]
[Please visit the related ArtAndScience picture gallery [Visitez la galerie d'images ArtAndScience associée]]
[Please visit the related DeterministicChaos picture gallery [Visitez la galerie d'images DeterministicChaos associée]]
[Please visit the related DeterministicFractalGeometry picture gallery [Visitez la galerie d'images DeterministicFractalGeometry associée]]

[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]]


Copyright © Jean-François COLONNA, 2010-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2010-2024.