A New Cost Function for Parameter Estimation of Chaotic Systems Using Return Maps as Fingerprints

Abstract

Estimating parameters of a model system using observed chaotic scalar time series data is a topic of active interest. To estimate these parameters requires a suitable similarity indicator between the observed and model systems. Many works have considered a similarity measure in the time domain, which has limitations because of sensitive dependence on initial conditions. On the other hand, there are features of chaotic systems that are not sensitive to initial conditions such as the topology of the strange attractor. We have used this feature to propose a new cost function for parameter estimation of chaotic models, and we show its efficacy for several simple chaotic systems.