A practical method to compute the largest Lyapunov exponent

It is a significant problem to determine whether a dynamical system present chaos, it could be solved by measuring the largest Lyapunov exponent of the system. Lyapunov exponents quantify the exponential divergence of the close phase-space trajectories and offer quantities to estimate the chaos. This article proposes a new method to calculate the largest Lyapunov exponent from experimental data. The method makes use of mutual information method and Cao's method to reconstruct the phase-space, and gets the largest Lyapunov exponent by Sano-Sawada method from computing Lyapunov exponent spectrum. This article also shows how stable and robust this new method practices comparing with other methods proven by large numbers of test.