The Parameter to Characterize Chaotic Dynamics

In this work, an asymptotic measure is introduced in order to characterize chaotic dynamics. This is the asymptotic distance between trajectories \math, which can actually help either as a complementary measure to Lyapunov exponents, or as an alternative parameter characterizing chaos when Lyapunov exponents are either very difficult, or impossible to work out. Some analytical relationships between the leading Lyapunov exponent and the values of \math both for discrete maps and continuous systems are here reported, together with experimental comparisons drawn from the simulation of Chua's circuit in different operational conditions.