Predictability of orbits in coupled systems through finite-time Lyapunov exponents - Juan C Vallejo; Miguel A F Sanjuán (New Journal of Physics, 2013)
The predictability of an orbit is a key issue when a physical model has strong sensitivity to the initial conditions and it is solved numerically. How close the computed chaotic orbits are to the real orbits can be characterized by the shadowing properties of the system. The finite-time Lyapunov exponents distributions allow us to derive the shadowing timescales of a given system. In this paper we show how to obtain information about the predictability of the orbits even when using arbitrary initial orientation for the initial deviation vectors. As a model to test our results, we use a system of two coupled Rössler oscillators. We analyze the dependence of the shadowing time on the coupling strength and internal nature of the oscillators. The main focus rests on the dependence of these results on the length of the finite-time intervals and the computation of the most appropriate interval for a better forecast. We emphasize the importance of extracting information from all of the relevant exponents to obtain an insight into the sources of the nonhyperbolicity of the system.