Synchronization Techniques for Chaotic Communication Systems

Jović, Branislav

doi:10.1007/978-3-642-21849-1

Cited by 63 publications

(51 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This is because it is often not easy to make all the characteristic modes fall right into such multiple disconnected synchronized intervals. There have been numerous results reported recently [Duan et al, 2009;Duan & Chen, 2011;Stefanski et al, 2007;Perlikowski et al, 2010;Jovic, 2011;Pikovsky et al, 2001]. (iv) The case of empty set.…”

Section: Network Synchronized Regions Based On Master Stability Functmentioning

confidence: 99%

“…In 1998, Pecora and Carroll initiated a master stability function approach to further investigate the complete synchronization in coupled identical oscillators [Pecora & Carroll, 1998]. Following this line, there are numerous results reported on the synchronization of coupled oscillators and complex networks [Arenas et al, 2008;Barahona & Pecora, 2002;Jovic, 2011;Park & Huang, 2007;Pikovsky et al, 2001;Wu, 2007]. In fact, the main idea of this approach is to transform the network synchronization problem into whether all the characteristic modes fall into the synchronized region, which is further determined by the master stability functions of coupled oscillators in complex networks.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bifurcation Analysis of Synchronized Regions in Complex Dynamical Networks

Tang

Lü

et al. 2012

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

This paper aims to investigate the bifurcation phenomena of synchronized regions in complex dynamical networks with varying node parameters and fixed inner-linking matrices. In particular, by using the unified chaotic system as network nodes, this paper further explores the bifurcation patterns of synchronized regions with synchronous states of both equilibrium points and attractors in complex dynamical networks based on two types of inner-linking matrices, respectively. Our results indicate that there does not exist any bifurcation phenomenon in the above synchronized regions for some specific inner-linking matrices. It means that the stability of network synchronous state will not change for some specific inner-linking matrices as the parameter of node dynamics changes. However, the above synchronized regions generate various bifurcation patterns for some inner-linking matrices and varying node parameters as follows: (i) The unbounded-empty set bifurcation mode; (ii) The bounded-empty set bifurcation mode; (iii) The single bounded-multiple bounded-single bounded-empty set bifurcation mode; (iv) The unbounded-multiple disconnected-empty set bifurcation mode. All these results tell us that the inner-linking matrices play a key role for determining the bifurcation patterns of synchronized regions.

show abstract

Section: Network Synchronized Regions Based On Master Stability Functmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of Synchronized Regions in Complex Dynamical Networks

Tang

Lü

et al. 2012

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

show abstract

“…This paper is concerned with the chaotic dynamics and synchronization of a reaction-diffusion system that assumes the same nonlinearities of the Newton-Leipnik system first proposed in [23] as a model of the rigid body motion through linear feedback (LFRBM). The dynamics of the original system as well as its control were studied in [24,25,26,28]. In [27], the authors examine a reaction-diffusion version of the system.…”

Section: Introductionmentioning

confidence: 99%

On the complete synchronization of a time-fractional reaction–diffusion system with the Newton–Leipnik nonlinearity

Mansouri

Bendoukha

Abdelmalek

et al. 2019

Applicable Analysis

View full text Add to dashboard Cite

In this paper, we consider a time-fractional reaction-diffusion system with the same nonlinearities of the Newton-Leipnik chaotic system. Through analytical tools and numerical results, we derive sufficient conditions for the asymptotic stability of the proposed model and show the existence of chaos. We also propose a nonlinear synchronization controller for a pair of systems and establish the local and global asymptotic convergence of the trajectories by means of fractional stability theory and the Lyapunov method.

show abstract

“…As a matter of fact, starting from publications by Fujisaka and Yamada [1] and later by Pecora and Carroll [2], there have been many explanations about the occurrence of this phenomenon as well as new practical applications [3]; among these we highlight [4]. For localized systems (ODE) the problem is well understood; see, for example, [4,5] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling

Acosta

García

Leiva

et al. 2017

International Journal of Differential Equations

View full text Add to dashboard Cite

We consider two reaction-diffusion equations connected by one-directional coupling function and study the synchronization problem in the case where the coupling function affects the driven system in some specific regions. We derive conditions that ensure that the evolution of the driven system closely tracks the evolution of the driver system at least for a finite time. The framework built to achieve our results is based on the study of an abstract ordinary differential equation in a suitable Hilbert space. As a specific application we consider the Gray-Scott equations and perform numerical simulations that are consistent with our main theoretical results.

show abstract

Synchronization Techniques for Chaotic Communication Systems

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 63 publications

References 0 publications

Bifurcation Analysis of Synchronized Regions in Complex Dynamical Networks

Bifurcation Analysis of Synchronized Regions in Complex Dynamical Networks

On the complete synchronization of a time-fractional reaction–diffusion system with the Newton–Leipnik nonlinearity

Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling

Contact Info

Product

Resources

About