ABSTRACT
This chapter deals with the particular case of linear systems which, and presents tools to analyze and characterizes the asymptotic behavior of solution near such sets. It describes that every physical system involves in its model some parameters which, when varying, may modify the qualitative properties of the solutions: which is the scope. Many physical modelling activities of the sixteenth century were conducted within the framework of infinitesimal calculus. These models are relations between variables which are functions of a special variable named "time" and their derivatives with respect to this time variable: these relations are ordinary differential equations. Remarkable sets can characterize configurations with minimal energy for a physical system. Stability property expresses the proximity of solutions throughout the evolution, but without guaranteeing convergence. A chaotic phenomenon can be obtained starting from several bifurcation phenomena: period doubling, bifurcation on the torus and intermittency.
