Variational Search of Periodic Motions in Complex Dynamical Systems

We present a method for the detection and characterization of periodic motions in the dynamics of complex systems. In contrast to other commonly used approaches, e.g., empirical orthogonal functions, principal oscillation patterns, singular spectrum analyses, this method is oriented towards scalar quantities, therefore, it does not require the introduction of an arbitrary metric in the space of the dynamical variables. Nonlinear effects are included; needless to say, the higher the non-linearities included the longer and more complicated the actual calculations become. We are trying the method on a Lorenz model and on a simple model of the dynamics of the atmosphere.