Dynamics characterization of modified Gross–Pitaevskii equation

The dynamics of dissipative and coherent N-body systems, such as a Bose–Einstein condensate, which can be described by an extended Gross–Pitaevskii formalism, is investigated. In order to analyze chaotic and unstable regimes, two approaches are considered: a metric one, based on calculations of Lyapunov exponents, and an algorithmic one, based on the Lempel–Ziv criterion. The consistency of both approaches is established, with the Lempel–Ziv algorithmic found as an efficient complementary approach to the metric one for the fast characterization of dynamical behaviors obtained from finite sequences.