An algorithm for estimating Lyapunov exponents of an unknown dynamical system is designed. The algorithm estimates not only the largest but all Lyapunov exponents of the unknown system. The estimation is carried out by a multivariate feedforward network estimation technique. We focus our attention on deterministic as well as noisy system estimation. The performance of the algorithm is very sati...

In 1892, the general problem of stability by the first approximation was considered by Lyapunov. He proved that if the system of the first approximation is regular and all its Lyapunov exponents (or characteristic exponents) are negative, then the solution of the original system is asymptotically Lyapunov stable. In 1930, it was stated by O. Perron that the requirement of regularity of the firs...

Lyapunov exponents measure the exponential rate of divergence of infinitesimally close orbits of a smooth dynamical system. These exponents are intimately related to the global stochastic behavior of the system and are fundamental invariants of a smooth dynamical system. In [EP], Eckmann and Procaccia suggested an analysis of Lyapunov exponents for chaotic dynamical systems. This suggestion was...

We consider a lattice of coupled circle maps, a popular model for the study of mode-locked phenomena. We find that the onset of spatiotemporal intermittency (STI) in this system is analogous to directed percolation (DP), with the transition being to a unique absorbing state for low nonlinearities, and to weakly chaotic absorbing states for high nonlinearities. We find that the complete set of s...