Synchronization Measure Based on a Geometric Approach to Attractor Embedding Using Finite Observation Windows

Abstract

A simple and effective algorithm for the identification of optimal time delays based on the geometrical properties of the embedded attractor is presented in this paper. A time series synchronization measure based on optimal time delays is derived. The approach is based on the comparison of optimal time delay sequences that are computed for segments of the considered time series. The proposed technique is validated using coupled chaotic Rössler systems.

A Meminductor-based Chaotic System

“…Simulation results show that the dynamic characteristics of this system are different from the other traditional chaotic systems with distinct dynamic behaviors. The complex chaotic signal generated by the simple meminductor chaotic system can be used in information encryption [20], analysis of physiological signals [7,18,25], communication security [1,30,16,17,32] and other fields.…”

A technique for estimating geometrical synchronization of biomedical signals

“…Geometrical similarity between two time series can be estimated via the algorithms developed and validated in [4,5]. A brief overview of those algorithms is presented below.…”

“…It was shown in [4,5] that the optimal time lag * can be used as a scalar feature representing the geometrical properties of the analyzed data signal. a) b) c) Fig.…”

“…In [4,5] we proposed a technique capable of estimating the degree of geometrical synchronization via near-optimal chaotic attractor embedding. In this paper, the measure is demonstrated and validated using the example of two coupled chaotic logistic maps.…”

Permutation Entropy Based on Non-Uniform Embedding

“…The optimal time delays are computed as the -dimensional argument of the following maximization problem [ 43 ]: where L is the upper range for all time lags.…”