Synchronization Of Spatiotemporal Chaos Research Articles

Controlling and synchronizing the spatiotemporal chaos of photorefractive ring oscillators with coupling

We present the control and synchronization of spatiotemporal chaos in the photo-refractive ring oscillator systems with coupling technology. First, we realize the synchronization of spatiotemporal chaos in the two photorefractive ring oscillator systems via mutual coupling by choosing a suitable coupling strength. With the mutual coupling strength enlarging, the two mutual coupling photorefractive ring oscillator systems are controlled into periodic state, period number differs on account of the coupling strength and lattice coordinates. By increasing the coupling strength, the photorefractive ring oscillator is converted into period 8, subsequently it is converted into periods 4 and 2, periodic synchronization of the photorefractive ring oscillator systems is achieved at the same time. Calculation results show that period 1 is impossible by mutual coupling technology. Then, we investigate the influence of noise and parameter deviation on chaotic synchronization. We find that mutual coupling chaotic synchronization method can synchronize two chaotic systems with the weak noise and parameter deviation and has very good robustness. Given that the weak noise and parameter deviation have a slight effect on synchronization. Furthermore, we investigate two dimension control and synchronization of spatiotemporal chaos in the photorefractive ring osillator systems with coupling technology and get successful results. Mutual coupling technology is suitable in practical photorefractive ring oscillator systems.

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures is investigated. The identification law of unknown parameters and the adaptive law of the configuration matrix element in state equations of network nodes are determined based on stability theory, and the conditions of realizing spatiotemporal chaos synchronization between uncertain complex networks with different structures are discussed and obtained. Further, the Fisher–Kolmogorov system with spatiotemporal chaotic behavior is taken as the nodes of drive and response networks to imitate the experiment. It is found that the synchronization performance between two networks is very stable.

Study on spatiotemporal chaos synchronization among complex networks with diverse structures

The spatiotemporal chaos synchronization among complex networks with diverse structures is investigated. The spatiotemporal chaos systems are taken as the nodes of networks and constructed as some networks with diverse structures. The conditions of global synchronization among networks and the coupling function to be determined among diverse networks are discussed and confirmed based on stability theory. The Burgers equation with many practice physics processes, such as turbulent flow and heat-transfer, is adopted for example to imitate the experiment. It is found that the synchronization performance among all networks is very stable.

Spatiotemporal chaos synchronization of complex networks by Backstepping design

Spatiotemporal chaos synchronization of complex networks by Backstepping design is investigated. Backstepping design is extended from synchronization between two chaotic systems to the synchronization of complex network constituted spatiotemporal chaotic systems. The relation between the configuration coefficient and the control gain is identified according to the stability theory. When the control input is added to any node of the network, the network synchronization is realized. Furthermore, simulation is made to verify the effectiveness of the synchronization mechanism.

Spatiotemporal chaos synchronization of an uncertain network based on sliding mode control

The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network. The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems. The sliding surface of the network and the control input are designed. Furthermore, the effectiveness of the method is analysed based on the stability theory. The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment. It is found that the synchronization performance of the network is very stable.

Network synchronization of spatiotemporal chaos and parameter identification in complex Ginzburg-Landau equation

The synchronization and the parameter identification of a complex network are studied, in which nodes are uncertain spatiotemporal chaos systems. The recognition laws of parameters are designed, and the unknown parameters in spatiotemporal chaos systems at the nodes of the complex network are identified. An appropriate Lyapunov function is constructed, and the conditions of realizing global synchronization of the network are discussed and confirmed based on the stability theory. The uncertain complex Ginzburg-Landau equation having spatiotemporal chaos behavior is taken as nodes in the complex network, and simulation results of spatiotemporal chaos synchronization and parameter identification show the effectiveness of the method.

Projective lag synchronization of spatiotemporal chaos via active sliding mode control

This paper investigates projective lag synchronization of spatiotemporal chaos with disturbances. A control scheme is designed via active sliding mode control. The synchronization of spatiotemporal chaos between a drive system and a response system with disturbances and time-delay is implemented by adding the active sliding mode controllers. The control law is applied to two identical spatiotemporal Gray–Scott systems. Numerical results demonstrate the feasibility and the effectiveness of the proposed approach.

The synchronization of spatiotemporal chaos of nearest-neighbor coupled network

The synchronization of spatiotemporal chaos in a nearest-neighbor coupled network is studied. Spatiotemporal chaos systems are taken as the nodes of the network,and the condition to realize global synchronization of the network is obtained by identifying the maximum Lyapunov exponent of the network according to Lyapunov stability theory. The nearest-neighbor coupled network with nodes of Fisher-Kolmogorov spatiotemporal chaos systems is taken as an example for simulation,the synchronization of spatiotemporal chaos for the network is checked. The synchronizing function of the network under bounded noise is further studied,and the results show that the method has good capability of anti-jamming.

Synchronization of spatiotemporal chaos in large scale rich-club network

The Plankton spatiotemporal chaos system is taken as network node and constructed as a rich-club network through nonlinear coupling. The synchronization of spatiotemporal chaos for the above network is investigated. The general selection rule of nonlinear coupling function connecting nodes in the rich-club network is presented. Furthermore, the condition to realize the network synchronization is analyzed theoretically based on Lyapunov stability theory. Finally, the synchronization effect of spatiotemporal chaos for the rich-club network is checked through artificial simulation. The results show that complete synchronization can be realized for all rich nodes in the rich-club network and all nodes in every subnetwork constructed in star-shape.

Synchronization of spatio-temporal chaos as an absorbing phase transition: a study in2+1 dimensions

The synchronization transition between two coupled replicas of spatio-temporal chaotic systems in2+1 dimensions is studied as a phase transition into an absorbingstate—the synchronized state. Confirming the scenario drawn in(1+1)-dimensional systems, the transition is found to belong to two different universalityclasses—multiplicative noise (MN) and directed percolation (DP)—depending on the linear ornonlinear character of damage spreading occurring in the coupled systems. By comparing acoupled map lattice with two different stochastic models, accurate numerical estimates for MN in2+1 dimensions are obtained. Finally, aiming to pave the way for future experimental studies,slightly non-identical replicas have been considered. It is shown that the presence of smalldifferences between the dynamics of the two replicas acts as an external field in the contextof absorbing phase transitions and can be characterized in terms of a suitable criticalexponent.

The synchronization of spatiotemporal chaos of all-to-all network using nonlinear coupling

N Fitzhugh-Nagumo models are used as network nodes, and synchronization of spatiotemporal chaos is studied using a all-to-all network constructed through a nonlinear coupling. The general principle of selecting coupling functions between nodes of the complex network is introduced. The theoretical analysis of the conditions for synchronization is made and the range of the feedback gain is obtained based on Lyapunov stability theory. The simulation is made to test the synchronization effect of the spatiotemporal chaos of the all-to-all network whose nodes are Fitzhugh-Nagumo models. The results show that the synchronization is fast and efficient, and the size of the network size has no sensitive effect on the stability of the network synchronization.

Lag synchronization of spatiotemporal chaos in a weighted network with ring connection

Lag synchronization of spatiotemporal chaos in a weighted network with ring connection is studied in this paper. Spatiotemporal chaos systems are taken as the nodes of the network，and connections between the nodes are made through a weighted ring. According to stability theory，the condition to realize lag synchronization of the network is obtained by identifying the maximum Lyapunov exponent of the network. Lag synchronization exists in the whole network when the largest Lyapunov exponent is less than zero，and the coupling strength between the nodes can be given any weight value. Autocatalytic reaction-diffusion chaotic systems are taken as the nodes of the network，and simulation results show the effectiveness of the method.

Synchronization of Spatiotemporal Chaos in Coupled Complex Ginzburg-Landau Oscillators**The project supported by National Natural Science Foundation of China, the Special Funds for Major State Basic Research Projects (G2000077304), the Huo Yingdong Foundation for Excellent Young Teachers, the Foundation for Excellent Doctoral Dissertation and the Foundation for University Key Teacher by the Ministry of Education of China

Synchronization of spatiotemporal distributed system is investigated by considering the model of 1D diffusively coupled complex Ginzburg–Landau oscillators. An itinerant approach is suggested to randomly move turbulent signal injections in the space of spatiotemporal chaos. Our numerical simulations show that perfect turbulence synchronization can be achieved with properly selected itinerant time and coupling intensity.

Chaos-based secure communications in a large community.

One-way coupled map lattices are used for cryptography in secure communication, based on spatiotemporal chaos synchronization. The sensitivity of synchronization between the encryption and decryption systems can be adjusted by varying the system size. With a suitable parameter combination, the cryptosystem can reach optimal trade-off of security and performance, i.e., it shows high security (resistant against the public-structure and known-plaintext attacks) together with fast encryption (and decryption) speed. An experiment of duplex voice transmission through university network is realized, which confirms the above advantages of our approach.

Unilaterally coupled synchronization of spatiotemporal chaos

Based on a coupled map lattice model, we present an approach of unilateral coupling to implement the synchronization of spatiotemporal chaos. Our numerical simulations show that the two spatiotemporal systems can accurately become synchronized by appropriately selecting the coupling strength and the equilibrium coefficient. We calculate the largest conditional Lyapunov exponent，so as to give the minimum coupling strength that can achieve the synchronization，and the functional relationship between the minimum coupling strength and the system parameters. The simulation results also indicate that this method is robust against noise.

DRIVING SYNCHRONIZATION OF SPATIOTEMPORAL CHAOS AND ITS APPLICATIONS IN CDMA COMMUNICATIONS

This paper investigates the driving synchronization of spatiotemporal chaos. Using this method, synchronization could be achieved efficiently. By improving the driving sequence generation method, the spatial periodicity in the original system is overcome. Large quantities of chaotic sequences are available, which possess the excellent properties expected in Code Division Multiple Access (CDMA) communications. These chaotic sequences can be used as the spreading sequences in place of the traditional pseudo-noise sequences. We also evaluate the performance of the chaotic CDMA communication systems and compute the average bit error rate caused by the multi-user interference and the noise in the channel. The theoretical and simulation results show the excellent performance of the scheme.

Synchronizing spatiotemporal chaos by introducing a finite flat region in the local map

An approach to synchronize spatiotemporal chaos is proposed. It is achieved by introducing a finite flat region in the local map. By using this scheme, a number of orbits in both the drive and the response subsystems are forced to pass through a fixed point in every dimension. With only an arbitrary phase space variable as drive signal, synchronization of spatiotemporal chaos can be achieved rapidly in the response subsystem. This is an advantage when compared with other synchronization methods that require a linear combination of the original phase space variables.

AN ENCRYPTION APPROACH TO DIGITAL COMMUNICATION BY USING SPATIOTEMPORAL CHAOS SYNCHRONIZATION

An encryption approach to digital communication by using spatiotemporal chaos synchronization is proposed. Two one-way coupled map lattice (OCOML) systems driven by a chaotic signal are synchronized. The chaotic outputs of the OCOML systems serve as the encryption and decryption keys and the main secret key is a set of coupling parameters of the OCOML. The advantages of the cryptosystem are its high communication efficiency, higher level of security and easy implementation by software. An example of duplex real-time voice communication between two computer users is described.

SPATIOTEMPORAL DYNAMICS OF COUPLED ARRAY OF MURALI–LAKSHMANAN–CHUA CIRCUITS

The circuit recently proposed by Murali, Lakshmanan and Chua (MLC) is one of the simplest nonautonomous nonlinear electronic circuits which show a variety of dynamical phenomena including various bifurcations, chaos and so on. In this paper we study the spatiotemporal dynamics in one- and two-dimensional arrays of coupled MLC circuits both in the absence as well as in the presence of external periodic forces. In the absence of any external force, the propagation phenomena of traveling wavefront and its failure have been observed from numerical simulations. We have shown that the propagation of the traveling wavefront is due to the loss of stability of the steady states (stationary front) via subcritical bifurcation coupled with the presence of neccessary basin of attraction of the steady states. We also study the effect of weak coupling on the propagation phenomenon in one-dimensional array which results in the blocking of wavefront due to the existence of a stationary front. Further we have observed the spontaneous formation of hexagonal patterns (with penta–hepta defects) due to Turing instability in the two-dimensional array. We show that a transition from hexagonal to rhombic structures occur by the influence of an external periodic force. We also show the transition from hexagons to rolls and hexagons to breathing (space-time periodic oscillations) motion in the presence of external periodic force. We further analyze the spatiotemporal chaotic dynamics of the coupled MLC circuits (in one dimension) under the influence of external periodic forcing. Here we note that the dynamics is critically dependent on the system size. Above a threshold size, a suppression of spatiotemporal chaos occurs, leading to a space-time regular (periodic) pattern eventhough the single MLC circuit itself shows a chaotic behavior. Below this critical size, however, a synchronization of spatiotemporal chaos is observed.

Coupled synchronization of spatiotemporal chaos

The synchronization of spatiotemporal chaos is very important in secure communication. In this paper, we present an approach of nonlinear coupling to implement the synchronization of spatiotemporal chaos. Two cases are considered. The first is the same systems with same parameters; the second is the same systems with different parameters. And the largest Lyapunov exponent spectra are calculated. Our numerical simulation shows that the mutual coupling can induce generalized synchronization.