ENVELOPE FOLLOWING BASED METHOD FOR THE COMPUTATION OF LYAPUNOV EXPONENTS IN ELECTRONIC CIRCUITS

Abstract

Lyapunov Exponents (LEs) can be considered as a statistical measure giving some approximate but signifficant insight in the behaviour of a dynamic system. If the systems we consider are models of realistic electronic circuits, we can reasonably assume them to be dissipative. LEs are useful to determine some general topological properties of the attractive region so that, even if the state space has a relatively large dimension, it is possible to foresee the presence of stable equilibrium points, periodic or quasi-periodic trajectories or, possibly, chaos. Lyapunov exponents and related measures such as the Lyapunov dimension are used to characterize the dynamics of complex systems and the geometrical properties of their trajectories in the state space. A few methods are available for the numerical computation of these measures and in most cases they are used only for systems that are normalized, well behaved and with a low dimensional state space. It is here proposed an approach that, being based on the envelope following method for the integration of stiff systems, can be efficiently used for the calculation of Lyapunov exponents and dimension in real electronic circuits.