Controlling based method for modelling chaotic dynamical systems from time series

摘要

A simple method is introduced for modelling chaotic dynamical systems from the time series, based on the concept of controlling of chaos by constant bias. In this method, a modified system is constructed by including some constants (controlling constants) into the given (original) system. The system parameters and the controlling constants are determined by solving a set of implicit nonlinear simultaneous algebraic equations which is obtained from the relation connecting original and modified systems. The method is also extended to find the form of the evolution equation of the system itself. The important advantage of the method is that it needs only a minimal number of time series data and is applicable to dynamical systems of any dimension. It also works extremely well even in the presence of noise in the time series. The method is illustrated in some specific systems of both discrete and continuous cases.