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:
                    R1  ==>  R1  ==>  R1  ==>  R1  ==>  R1  ==>  R1

/\ || || \/
R3 R2
/\ || || \/
R3 R2
/\ || || \/
R3 R2
/\ || || \/
R3 <== R3 <== R3 <== R2 <== R2 <== R2
where {R1,R2,R3} are respectively the three coordinates of the current point inside the following domain [3.363,3.636]x[3.450,3.650]x[2.600,3.600]. Only the points corresponding to a dynamical system with a negative Lyapunov exponent are displayed.


See a set of 4x3 stereograms:




See a bidimensionnal dynamics:




(CMAP28 WWW site: this page was created on 11/16/2010 and last updated on 10/27/2015 10:53:24 -CET-)



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

[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 AVirtualSpaceTimeTravelMachine [Retour à AVirtualSpaceTimeTravelMachine]]
[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 (c) Jean-François Colonna, 2010-2015.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2010-2015.