Estimation of the Largest Lyapunov Exponent for a Model of Cross-Shaped Waves in a Rectangular Channel of Finite Size

The largest Lyapunov exponent characterizes the degree of exponential divergence of close trajectories of a dynamical system. The presence of a positive Lyapunov exponent in the system reveals rapid divergence of any two arbitrarily close trajectories with time and sensitivity to the values of the initial conditions. Therefore, as a result of determination of the Lyapunov exponent, it becomes possible to identify the system in a sense of chaotic dynamics. We propose a method for increasing the accuracy of the Benettin numerical algorithm aimed at the evaluation of the largest Lyapunov exponent in the case of a dissipative dynamical system. The results of calculations are presented for the hydrodynamic model of cross-shaped waves in a rectangular channel of finite size.