Measure of orbital stickiness and chaos strength

Patterns can be used effectively to characterize dynamical orbits as regular or chaotic. The proposed method focuses on local, epochal characterization of orbits as opposed to global characterization usually employed by most established measures. The “patterns method” provides essentially a measure of chaos strength for every extremum of a signal. For this reason, it provides information about sticky epochs of chaotic orbits, as well as time-dependent orbits. This way it can be used to give extremely detailed pictures of the phase space of a system, as well as to provide characterizations early in the evolution of orbits. Moreover, the method applies generally; all that is required is a signal, of which an orbit is merely an example.