Estimation of System Parameters and Predicting the Flow Function from Time Series of Continuous Dynamical Systems

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given (original) system. Then the system parameters and the controlling constants are determined by solving a set of nonlinear simultaneous algebraic equations obtained from the relation connecting original and modified systems. Finally, the method is extended to find the form of the evolution equation of the system itself. The major 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. The method also works extremely well even in the presence of noise in the time series. This method is illustrated for the case of Lorenz system.