Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback

In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.

A novel pseudo-random coupled LP spatiotemporal chaos and its application in image encryption

In this paper, first, we investigate a novel one-dimensional logistic-PWLCM（LP） modulation map which is derived from the logistic and PWLCM maps. Second, we propose a novel PCLML spatiotemporal chaos in pseudo-random coupling method that can accelerate the system behavior of the fully spatial chaos. Here, because the better chaotic properties include a wide range of parameter settings and better ergodicity than a logistic map, the LP is used in PCLML as f（x）. The Kolmogorov–Sinai entropy density and universality and the bifurcation diagram are employed to investigate the chaotic behaviors of the proposed PCLML model. Finally, we apply the LP and PCLML chaotic systems to image encryption to improve the effectiveness and security of the encryption scheme. By combining self-generating matrix model M and dynamic substitution box（S-Box） methods, we design a new image encryption algorithm. Numerical simulations and security analysis have been carried out to demonstrate that the proposed algorithm has a high security level and can efficiently encrypt several different kinds of images into random-like images.

A self-adapting image encryption algorithm based on spatiotemporal chaos and ergodic matrix

To ensure the security of a digital image, a new self-adapting encryption algorithm based on the spatiotemporal chaos and ergodic matrix is proposed in this paper. First, the plain-image is divided into different blocks of the same size, and each block is sorted in ascending order to obtain the corresponding standard ergodic matrix. Then each block is encrypted by the spatiotemporal chaotic system and shuffled according to the standard ergodic matrix. Finally, all modules are rearranged to acquire the final encrypted image. In particular, the plain-image information is used in the initial conditions of the spatiotemporal chaos and the ergodic matrices, so different plain-images will be encrypted to obtain different cipherimages. Theoretical analysis and simulation results indicate that the performance and security of the proposed encryption scheme can encrypt the image effectively and resist various typical attacks.

The signal synchronization transmission of a spatiotemporal chaos network constituted by a laser phase-conjugate wave

The signal synchronization transmission of a spatiotemporal chaos network is investigated. The structure of the coupling function between connected nodes of the complex network and the value range of the linear term coefficient of the separated configuration in state equation of the node are obtained through constructing an appropriate Lyapunov function. Each node of the complex network is a laser spatiotemporal chaos model in which the phase-conjugate wave and the unilateral coupled map lattice are taken as a local function and a spatially extended system, respectively. The simulation results show the effectiveness of the signal synchronization transmission principle of the network.

Security analysis of a one-way hash function based on spatiotemporal chaos

The collision and statistical properties of a one-way hash function based on spatiotemporal chaos are investigated. Analysis and simulation results indicate that collisions exist in the original algorithm and, therefore, the original algorithm is insecure and vulnerable. An improved algorithm is proposed to avoid the collisions.

Secure communication based on spatiotemporal chaos

In this paper, we propose a novel approach to secure communication based on spatiotemporal chaos. At the transmitter end, the state variables of the coupled map lattice system are divided into two groups: one is used as the key to encrypt the plaintext in the N-shift encryption function, and the other is used to mix with the output of the N-shift function to further confuse the information to transmit. At the receiver end, the receiver lattices are driven by the received signal to synchronize with the transmitter lattices and an inverse procedure of the encoding is conducted to decode the information.Numerical simulation and experiment based on the TI TMS320C6713 Digital Signal Processor(DSP) show the feasibility and the validity of the proposed scheme.

An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree

This paper proposes an image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree.Firstly,other programming software is used to perform the middle order traversal,and the plaintext image is sorted according to the middle order traversal sequence on the permutation.Secondly,the chaotic sequence is generated using the coupled map lattice to set the chaotic interference value.Finally,the XOR operation between the adjacent pixel values of the replacement image is completed to generate the ciphertext matrix.The simulation and experimental results show that the proposed algorithm can resist typical attacks and has good robustness.

Cryptanalysis on an image block encryption algorithm based on spatiotemporal chaos

An image block encryption scheme based on spatiotemporal chaos has been proposed recently. In this paper, we analyse the security weakness of the proposal. The main problem of the original scheme is that the generated keystream remains unchanged for encrypting every image. Based on the flaws, we demonstrate a chosen plaintext attack for revealing the equivalent keys with only 6 pairs of plaintext/ciphertext used. Finally, experimental results show the validity of our attack.

Elimination of spiral waves and spatiotemporal chaos by the pulse with a specific spatiotemporal configuration

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time （to）. When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications.

ON CML MODEL FOR STUDY OF SPATIOTEMPORAL CHAOS

A new coupled map lattic (CML) model is given by using some stability analysis for the related difference equations. Numerical results show that the new model is an effective one of studying spatiotemporal chaos, especially for strongly coupled systems.

CONVECTIVE COUPLED MAP FOR SIMULATING SPATIOTEMPORAL CHAOS IN FLOWS

A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid hows can be envisaged.

Synchronization of spatiotemporal chaos in a class of complex dynamical networks

This paper studies the synchronization of complex dynamical networks constructed by spatiotemporal chaotic systems with unknown parameters. The state variables in the systems with uncertain parameters are used to construct the parameter recognizers, and the unknown parameters are identified. Uncertain spatiotemporal chaotic systems are taken as the nodes of complex dynamical networks, connection among the nodes of all the spatiotemporal chaotic systems is of nonlinear coupling. The structure of the coupling functions between the connected nodes and the control gain are obtained based on Lyapunov stability theory. It is seen that stable chaos synchronization exists in the whole network when the control gain is in a certain range. The Gray-Scott models which have spatiotemporal chaotic behaviour are taken as examples for simulation and the results show that the method is very effective.

Elimination of spiral waves and spatiotemporal chaos by the synchronization transmission technology of network signals

A method to eliminate spiral waves and spatiotemporal chaos by using the synchronization transmission technology of network signals is proposed in this paper. The character of the spiral waves and the spatiotemporal chaos in the Fitzhugh-Nagumo model is presented. The network error evolution equation with spatiotemporal variables and the corresponding eigenvalue equation are determined based on the stability theory, and the global synchronization condition is obtained. Simulations are made in a complex network with Fitzhugh-Nagumo models as the nodes to verify the effectiveness of the synchronization transmission principle of the network signal.

Synchronization of spatiotemporal chaos in complex networks via backstepping

A backstepping approach is proposed for the synchronization of chain networks of multi-spatiotemporal chaotic systems with topologically equivalent structures. The synchronization of multi-spatiotemporal chaotic systems is imple- merited by adding the control only to a terminal node, and the controller is designed via a corresponding update law. The control law is applied to spatiotemporal Gray-Scott systems. Numerical results demonstrate the effectiveness and the feasibility of the proposed approach.

Projective synchronization of spatiotemporal chaos in a weighted complex network

Projective synchronization of a weighted complex network is studied in which nodes are spatiotemporal chaos systems and all nodes are coupled not with the nonlinear terms of the system but through a weighted connection. The range of the linear coefficient matrix of separated configuration, when the synchronization is implemented, is determined according to Lyapunov stability theory. It is found that projective synchronization can be realized for unidirectional star-connection even if the coupling strength between the nodes is a given arbitrary weight value. The Gray-Scott models having spatiotemporal Chaos behaviours are taken as nodes in the weighted complex network, and simulation results of spatiotemporal synchronization show the effectiveness of the method.

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.

One-way hash function construction based on the spatiotemporal chaotic system

Based on the spatiotemporal chaotic system, a novel algorithm for constructing a one-way hash function is proposed and analysed. The message is divided into fixed length blocks. Each message block is processed by the hash compression function in parallel. The hash compression is constructed based on the spatiotemporal chaos. In each message block, the ASCII code and its position in the whole message block chain constitute the initial conditions and the key of the hash compression function. The final hash value is generated by further compressing the mixed result of all the hash compression vulues. Theoretic analyses and numerical simulations show that the proposed algorithm presents high sensitivity to the message and key, good statistical properties, and strong collision resistance.

Evaluating the dynamical coupling between spatiotemporally chaotic signals via an information theory approach

An information-theoretic measure is introduced for evaluating the dynamical coupling of spatiotemporally chaotic signals produced by extended systems. The measure of the one-way coupled map lattices and the one-dimensional, homogeneous, diffusively coupled map lattices is computed with the symbolic analysis method. The numerical results show that the information measure is applicable to determining the dynamical coupling between two directly coupled or indirectly coupled chaotic signals.

Control Chaos of a Unidirectionally Traffic Coupled Map Lattice Model

Spatiotemporal chaos is studied by using the unidirectional traffic coupled lattice model with hyperbolic tangent local map. The coupled map lattice (CML) model can simulate the complex traffic flow phenomenon which is similar to the traditional traffic flow model. The nonlinear feedback method is used to study the control of the chaotic system of the unidirectionally traffic coupled map lattice model. The stability of spatiotemporal chaos in the coupled map lattice is realized. The results of numerical simulation show that there is a relationship between control results and control parameters when controlling spatiotemporal chaos to a uniform stable state in a certain phase space compression parameter region.

Non-Local Coupling and Partial Synchronization in Chaotic Systems

Partial synchronization （PaS） on regular networks with a few non-local couplings are studied. The criterion that PaS can emerge in any given network and some relevant phenomena about Lyapunov exponents are found. Theoretical and numerical analysis show that the non-local coupling is the key mechanism of the emergence of PaS.