Validating the physical model of a chaotic system by topological analysis

Topological analysis is employed for the first time to our knowledge as a method of validation for a physical model describing a chaotic system. Topological analysis theory provides both away to characterize the topological structure of chaotic attractors by means of a set of integer numbers and a method to obtain this set departing from a time series generated by the chaotic system. The validation method proposed here consists of comparing the topological structure of chaotic attractors obtained from time series generated on the one hand by an experimental system and on the other hand by the numerical model under test. This procedure has been applied to an erbium-doped fiber laser subject to pump power sine-wave modulation.