Synchronization in random networks with given expected degree sequences

Synchronization in random networks with given expected degree sequences is studied. We also investigate in details the synchronization in networks whose topology is described by classical random graphs, power-law random graphs and hybrid graphs when N goes to infinity. In particular, we show that random graphs almost surely synchronize. We also show that adding small number of global edges to a local graph makes the corresponding hybrid graph to synchroniz

Synchronization in Networks of Hindmarsh-Rose Neurons

Synchronization is deemed to play an important role in information processing in many neuronal systems. In this work, using a well known technique due to Pecora and Carroll, we investigate the existence of a synchronous state and the bifurcation diagram of a network of synaptically coupled neurons described by the Hindmarsh-Rose model. Through the analysis of the bifurcation diagram, the different dynamics of the possible synchronous states are evidenced. Furthermore, the influence of the topology on the synchronization properties of the network is shown through an exampl

Synchronization of Random Linear Maps

We study synchronization of random one-dimensional linear maps for which the Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of these maps are explained using their relation with a random walk. We confirm that the Lyapunov exponent changes sign at the complete synchronization transition. We also consider partial synchronization of nonidentical systems. It turns out that the way partial synchronization manifests depends on the type of differences (in Lyapunov exponent or in contraction points) between the systems. The crossover from partial synchronization to complete synchronization is also examined.Comment: 5 pages, 6 figure

Synchronization in random networks with given expected degree sequences

Synchronization in random networks with given expected degree sequences is studied. We also investigate in details the synchronization in networks whose topology is described by classical random graphs, power-law random graphs and hybrid graphs when N goes to infinity. In particular, we show that random graphs almost surely synchronize. We also show that adding small number of global edges to a local graph makes the corresponding hybrid graph to synchronize

Synchronization and directed percolation in coupled map lattices

We study a synchronization mechanism, based on one-way coupling of all-or-nothing type, applied to coupled map lattices with several different local rules. By analyzing the metric and the topological distance between the two systems, we found two different regimes: a strong chaos phase in which the transition has a directed percolation character and a weak chaos phase in which the synchronization transition occurs abruptly. We are able to derive some analytical approximations for the location of the transition point and the critical properties of the system. We propose to use the characteristics of this transition as indicators of the spatial propagation of chaoticity.Comment: 12 pages + 12 figure

Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption

Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which adds enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.Comment: 20 pages, 11 figures; Article in press, Optics Communications (2011

A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application to Watermarking

In this paper, a new chaotic pseudo-random number generator (PRNG) is proposed. It combines the well-known ISAAC and XORshift generators with chaotic iterations. This PRNG possesses important properties of topological chaos and can successfully pass NIST and TestU01 batteries of tests. This makes our generator suitable for information security applications like cryptography. As an illustrative example, an application in the field of watermarking is presented.Comment: 11 pages, 7 figures, In WISM 2010, Int. Conf. on Web Information Systems and Mining, volume 6318 of LNCS, Sanya, China, pages 202--211, October 201

Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization

We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and coupling-enhancement are provided. We apply these algorithms to the self-organized synchronization of two coupled Lorenz systems. It is found that after a long-time self-organized process, the two coupled chaotic systems can achieve synchronization with almost minimum required coupling-speed ratio.Comment: 4 pages, 5 figure