One Method for Restoring Inhomogeneous Attractors

Abstract

Several methods of restoration of phase portraits were applied to real experimental realizations a(t) of biological origin. The algorithms for global reconstruction were used to create qualitative models of the regimes under study. The results of global modeling were satisfactory for the time series of simple shape, but in case of complicated inhomogeneous realizations the traditional algorithms did not give reasonable models. We suggest a method for restoration of inhomogeneous attractors on a(t) as follows: [Formula: see text] while the other coordinates could be restored by any known methods (delay, differentiation, etc.). Such a representation of the attractor's coordinates preserves a simple form of the first equation of the system of differential equations sought [Formula: see text]This method was tested first on an artificially produced inhomogeneous realization containing pieces with very slow and very quick motion. After that it was successfully applied to real biological inhomogeneous realizations.