One method of restoring ingomogenous attractors
V.S. Anishchenko, N.B. Janson, A.N. Pavlov
Saratov State University, Saratov, Russia
Several methods of restoration of phase portraits were applied to real experimental realizations a(t) of biological origin. The algorithms of 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 the case of complicated inhomogenous realizations the traditional algorithms did not give reasonable models. We suggested a method for restoration of inhomogenous attractors on (a(t) as follows:
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 equation sought.
This method was tested first on an artificially produced inhomogenous realization containing pieces with very slow and very quick motion. After that it was successfully applied to real biological inhomogenous realizations.