  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.
