Meta-dynamical adaptive systems and their applications to a fractal algorithm and a biological model

Emmanuel Moulay (1, 2) , Marc Baguelin (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
3 Department of Zoology

In this article, one defines two models of adaptive systems: the meta-dynamical adaptive system using the notion of Kalman dynamical systems and the adaptive differential equations using the notion of variable dimension spaces. This concept of variable dimension spaces relates the notion of spaces to the notion of dimensions. First, a computational model of the Douady's Rabbit fractal is obtained by using the meta-dynamical adaptive system concept. Then, we focus on a defense-attack biological model described by our two formalisms.

Mots clés: fractal algorithm; dynamical systems; adaptive systems; biological systems; fractal algorithm.

Domaines: Adaptation et Systèmes auto-organisés [nlin.AO]; Dynamique Chaotique [nlin.CD]

Emmanuel Moulay, Marc Baguelin. Meta-dynamical adaptive systems and their applications to a fractal algorithm and a biological model. Physica D: Nonlinear Phenomena, 2005, 207, pp.79-90. ⟨10.1016/j.physd.2005.05.013⟩. ⟨hal-00136495⟩