Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces

Dynamics of driven dissipative Frenkel-Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of system in the presence of external forces is examined by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to estimate the system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is standard sinusoidal one, calculation of the largest Lyapunov exponent offers the most accurate way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points at an interesting advantage of this technique since even just by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the behavior of the system when driving forces are applied.