Effect of noise on generalized synchronization of chaos: theory and experiment

Abstract

The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized synchronization is shown to possess a great stability with respect to noise. The reasons of the revealed particularity are explained by means of the modified system approach [A. E. Hramov, A. A. Koronovskii, Phys. Rev. E. 71, 067201 (2005)] and confirmed by the results of numerical calculations and experimental studies. The main results are illustrated using the examples of unidirectionally coupled chaotic oscillators and discrete maps as well as spatially extended dynamical systems. Different types of the model noise are analyzed. Possible applications of the revealed particularity are briefly discussed. PACS. XX.XX.XX No PACS code given practical applications where the level of natural noise is sufficient. The structure of the paper is as follows. Section 1 contains brief description of the generalized synchronization regime, its methods for detection and mechanisms of its arising both in the cases of the absence and presence of noise. The reasons of the stability of the generalized synchronization regime with respect to noise are also discussed in this section. Section 2 presents results of numerical simulation of the influence of noise on the threshold of the synchronous regime arising in several systems with discrete and continuous time as well as spatially extended systems demonstrating spatio-temporal chaos. In Section 3 we describe the experimental setup for the observation of the generalized synchronization regime in the presence of noise in the electronic chaotic circuit and give the results obtained by means of it. Final discussions and remarks are given in Conclusions.

Binary generalized synchronization

“…This kind of synchronous behavior means the state vectors of the interacting chaotic systems being in the generalized synchronization regime are related with each other. It has been observed in many systems both numerically [43,[49][50][51] and experimentally [46,52,53].…”

“…In numerical experiments on the BGS such processes can be simulated by the addition of noise in the systems under study or by the control parameter mismatch [67]. At the same time, as well as the GS of unidirectionally coupled chaotic systems (see, e.g., [46]), the BGS regime possess a great enough stability to the external perturbations. In such case the stability of the synchronous regime is defined by the stability of the GS regime established between the hidden variables of interacting systems just in the same way as for the GS phenomenon [46].…”

“…At the same time, as well as the GS of unidirectionally coupled chaotic systems (see, e.g., [46]), the BGS regime possess a great enough stability to the external perturbations. In such case the stability of the synchronous regime is defined by the stability of the GS regime established between the hidden variables of interacting systems just in the same way as for the GS phenomenon [46]. At the same time, since the type of coupling between interacting systems considered in [46] is different in comparison with the system under study, the quantitative values of the boundaries of GS and BGS regime stability are also differed.…”

“…Among the different types of the synchronous behavior of chaotic systems the generalized synchronization (GS) [25,26,42] stands out due to its interesting features [43][44][45][46] and possible applications [18,47,48]. This kind of synchronous behavior means the state vectors of the interacting chaotic systems being in the generalized synchronization regime are related with each other.…”

Метод Выделения Характерных Фаз Поведения В Сложных Сетях, Находящихся В Режиме Перемежающейся Обобщенной Синхронизации

“…На настоящий момент явление обобщенной синхронизации доволь-но подробно изучено на примере широкого круга взаимодействующих систем: исследованы как системы с дискретным временем, связанные однонаправленно и взаимно [8,9], так и потоковые системы с однона-правленной [10,11] и взаимной [5] связью (включая пространственно-распределенные системы [12]). Следующим этапом в исследовании явления обобщенной хаотической синхронизации стало рассмотрение сетей нелинейных элементов со сложной топологией связей [13], в частности, был изучен процесс установления режима обобщенной синхронизации при переходе от асинхронной динамики к синхронной в малой сети логистических отображений [14].…”