Diagnostics and measurement of chaotic synchronization in the presence of noise

The research is devoted to a method of diagnostics and quantitative analysis of chaotic synchronization in the presence of noise. We analyze how the additive white normal noise influences the accuracy of the measurement of synchronization of chaos. We also propose a new modification of the standard algorithm, which significantly reduces the sensitivity of the method to the noise. Importance of the study is caused by its perspectives for fundamental researches of general properties of chaotic synchronization, as well as for practical applications to searching interconnections between oscillations in systems of different nature. This is especially important in biological and medical investigations where the level of noise is 38 usually very large and the interference can not be removed. Thus, possibility of measuring of the level of interconnection between oscillations in different biological samples allows to detect hidden mechanisms existing between them. The researches are carried out by the method of numerical simulations. The model under study is a system of two uni-directionally coupled logistic maps, which is one of the most simple model in the nonlinear dynamics. From the other side, it allows to explore all general properties of coupled self-sustained oscillators with period-doubling bifurcations. The results of the researches have demonstrates that the basic correlative method of measurement of chaotic synchronization is valid only when the noise is absent or very small. The proposed in the work algorithm, which is based on using time lag between the estimated signals, can significantly improve the accuracy of measurements in the presence of noise. It can be applied to measurement of chaotic synchronization for a wide class of dynamical systems, in the cases when the statistical properties of chaotic attractors remain similar for both synchronous and non-synchronous regimes.