Spatiotemporal Chaos Model Research Articles

Short message encryption technology of Beidou communication based on SM9

AbstractTo reduce the security authentication time cost, forwarding delay, and enhance message security of Beidou communication short messages, this paper proposes a Beidou communication short message encryption technology based on SM9 (Mobile Code Secure Communication). This technology uses split hierarchical clustering algorithm to cluster the short message data of Beidou Communication, in order to unify the processing of similar short message data and improve the encryption efficiency of subsequent short messages. Based on the data clustering results, this paper constructs a short message forwarding verification model using the SM9 identification password algorithm, and provides the message content of the communication application protocol and the communication receiving information protocol to achieve low‐cost and efficient forwarding verification. In addition, this article improves the initial value selection of Logistic chaotic mapping by coupling the tent map with coupled mapping lattice (CML) in the spatiotemporal chaos model to generate a chaotic initial value sequence, thereby expanding the key space, enhancing the ability to resist exhaustive attacks, enhancing the randomness of the generated key parameters, and optimizing the encryption effect of short messages. The experimental results show that the short message security authentication time of the technology proposed in this article is basically controlled within 25 ms, and the minimum forwarding delay is only 23.9 ms, which can effectively resist attacks and improve the security of Beidou communication.

Mutil-medical image encryption by a new spatiotemporal chaos model and DNA new computing for information security

Mutil-medical image encryption by a new spatiotemporal chaos model and DNA new computing for information security

A new spatiotemporal chaos model and its application in bit-level image encryption

A new spatiotemporal chaos model and its application in bit-level image encryption

Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typically exhibits memory effects. Recent work has found a variety of data-driven model reduction methods to be effective for representing such non-Markovian dynamics, but their scope and dynamical underpinning remain incompletely understood. Here, we study data-driven model reduction from a dynamical systems perspective. For both chaotic and randomly-forced systems, we show the problem can be naturally formulated within the framework of Koopman operators and the Mori-Zwanzig projection operator formalism. We give a heuristic derivation of a NARMAX (Nonlinear Auto-Regressive Moving Average with eXogenous input) model from an underlying dynamical model. The derivation is based on a simple construction we call Wiener projection, which links Mori-Zwanzig theory to both NARMAX and to classical Wiener filtering. We apply these ideas to the Kuramoto-Sivashinsky model of spatiotemporal chaos and a viscous Burgers equation with stochastic forcing.

A new image encryption scheme based on coupling map lattices with mixed multi-chaos

As a kind of spatiotemporal chaos, coupled map lattice (CML) is widely applied into image encryption because of its advantages of more complex dynamical behavior and lower computational overhead. Firstly, this paper proposed a novel spatiotemporal chaos model (MCML) by mixing Logistic, Sine and Tent maps into CML map together. Beyond that, we also change the structure of CML and the coupling method in different lattices. Bifurcation diagram, Lyapunov exponents and NIST test are employed to measure the chaotic behaviors of the MCML system. Secondly, by applying MCML chaos, we design a new key binding and distribution rule, the improved diffusion scheme to encrypt image. Furthermore, the novel bit Z-scan scrambling method also be used to enhance the security of the encryption scheme. Finally, a large number of experimental results prove that our proposed scheme is suitable for image encryption and has high security against common attacks.

Spatiotemporal Chaos in Coupled Logistic Map Lattice With Dynamic Coupling Coefficient and its Application in Image Encryption

This paper proposes a new spatiotemporal chaos model, which is a logistic-dynamic coupled logistic map lattice (LDCML). Through a large number of simulation experiments and theoretical analysis, it can be proved that a chaotic region has the larger parameter space, and the system is more chaotic compared with traditional CML by the introduction of a dynamic coupled method, which is more suitable for chaotic encryption and secure communications. So, this paper presents a bit-level adaptive image encryption algorithm based on this system, and further demonstrates the good chaos of the system from the aspect of encryption performance.

Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems.

We present an alternative methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. We show that with an appropriate choice of time-dependent controls we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, traveling waves (single and multipulse ones or bound states), and spatiotemporal chaos. We exemplify our methodology with the generalized Kuramoto-Sivashinsky equation, a paradigmatic model of spatiotemporal chaos, which is known to exhibit a rich spectrum of wave forms and wave transitions and a rich variety of spatiotemporal structures.

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.

Spatiotemporal chaos anti-synchronization of a complex network with different nodes

Anti-synchronization of complex network is investigated in which nodes are discrete spatiotemporal chaos systems with diverse structures. The form of the coupling functions connecting nodes in the complex network and the control gain are obtained through constructing an appropriate Lyapunov function. The spatially extended system of laser phase conjugate wave having spatiotemporal chaos behavior in physics, Gibbs electrical-optical spatiotemporal chaos model, Bragg acousto-optical spatiotemporal chaos model and the one-dimensional discrete convective equation are all taken as nodes of the complex network. Artificial results show that a stable anti-synchronization is obtained in the whole network.

Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network

Synchronization and parameter identification of a unidirectional star-network constructed by discrete spatiotemporal chaos systems with unknown parameters are studied. The synchronization principle of the network and design method of parameter recognition law are introduced. The function to be determined in the parameter recognition law and the range of adjusting parameter are obtained based on Lyapunov stability theory. Not only global synchronization of the network is realized, but also the unknown parameters in spatiotemporal chaos systems at the nodes of the network are identified. Discrete laser spatiotemporal chaos model is taken as each node of the network, and simulation results show the effectiveness of the synchronization principle and parameter recognition law.

Projective synchronization of a weighted network in a laser spatiotemporal chaos model

A method is introduced to realize spatiotemporal chaos projective synchronization for a weighted network. The coupling function between connected nodes of the weighted network is derived and the range of the linear coefficient matrix of separated configuration in state equation of the node is obtained through constructing an appropriate Lyapunov function. Each node of the weight network is a laser spatiotemporal chaos model in which Bragg acousto-optical bistable system and unilateral coupled map lattices are taken as the local function and the spatial extended system, respectively. The projective synchronization effect of the weighted network is checked by numerical emulation. The results show that projective synchronization can be realized even if the coupling strength between the nodes are given arbitrary weight values.

Real-time deterministic chaos control by means of selected evolutionary techniques

This contribution introduces continuation of an investigation on deterministic spatiotemporal chaos real-time control by means of selected evolutionary techniques. Real-time-like behavior is specially defined and simulated with the spatiotemporal chaos model based on mutually nonlinearly joined n equations, so-called coupled map lattices (CML). Four evolutionary algorithms are used for chaos control here: differential evolution, self-organizing migrating algorithm, genetic algorithm and simulated annealing in a total of 12 versions. For modeling of real-time spatiotemporal chaos behavior, the so-called CML were used based on logistic equation to generate chaos. The main aim of this investigation was to show that evolutionary algorithms, under certain conditions, are capable of real-time control of deterministic chaos, when the cost function is properly defined as well as parameters of selected evolutionary algorithm. Investigation consists of four different case studies with increasing simulation complexity. For all algorithms, each simulation was repeated 100 times to show and check robustness of used methods. All data were processed and used in order to get summarizing results and graphs.

Existence and nonexistence of a global solution to the Kuramoto-Sivashinsky equation

1 We consider initial boundary-value problems (IBV) for the Kuramoto‐Sivashinsky equation in one dimension. We prove the existence of global solution both with Dirichlet and with “Navier” boundary conditions. Then we prove a blow-up of solutions of IBV problem with boundary conditions of other kind. It is well known the role of the Kuramoto‐Sivashinsky equation in the contemporary nonlinear mechanics and physics. This equation arises as a model in hydrodynamics (thin film flow down an inclined plane in the presence of an electric field), in the combustion theory (propagation of flame fronts), phase turbulence and plasmas, as one model for spatiotemporal chaos and in many other physical phenomena.

INVESTIGATION ON REALTIME DETERMINISTIC CHAOS CONTROL BY MEANS OF EVOLUTIONARY ALGORITHMS

This contribution introduces an investigation on deterministic spatiotemporal chaos real-time control, based on evolutionary algorithms use. Problem is defined so that spatiotemporal chaos model would behave like real-time process. Two evolutionary algorithms are used for chaos control here: differential evolution and self-organizing migrating algorithm in total number of 10 versions (SOMA in 4, DE in 6). Like a model of spatiotemporal chaos so called coupled map lattices based on logistic equation are used. Main aim of this investigation was to show that evolutionary algorithms are capable of real-time control of deterministic chaos when cost function is properly defined. Investigation consists of three different case studies with increasing calculation complexity. For both algorithms each simulation was 100 times repeated to show and check robustness of used methods.

INVESTIGATION ON EVOLUTIONARY DETERMINISTIC CHAOS CONTROL

This contribution introduces an investigation on deterministic spatiotemporal chaos control based on evolutionary algorithms use. Two evolutionary algorithms are used for chaos control here: differential evolution and self-organizing migrating algorithm. Like a model of spatiotemporal chaos so called coupled map lattices are used. Main aim of this investigation was to show that evolutionary algorithms are capable of deterministic chaos control when cost function is properly defined. Investigation consists of four different case studies with increasing calculation complexity. For both algorithms each simulation was 50 times repeated to show and check robustness of used methods.

Convective Lyapunov Exponents and Propagation of Correlations

We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a Hamiltonian system (a Fermi-Pasta-Ulam chain of oscillators); (ii) a general model for spatiotemporal chaos (the complex Ginzburg-Landau equation); (iii) experimental data taken from a CO2 laser with delayed feedback. In the last case, the convective Lyapunov exponent is determined directly from the experimental data.

Unstable periodic orbits in the presence of spatio-temporal chaos

In this paper we investigate spatio-temporal disorder in a liquid crystal light valve with two-dimensional feedback and modulated input. We focus on the specific case of an optical feedback with a 180° rotation. By modulating the input field with appropriate amplitude and frequency, chaotic domains are formed in different locations of the transverse space [1, 2]. Because of diffusion, a global description of the spatio-temporal dynamics requires a partial differential equation. However, the local dynamics of the chaotic domains can be embedded in low-dimensional manifolds. The detection of a variety of different unstable periodic orbits (UPOs) at different spatial locations and the presence of UPOs for different detector sizes are strong indications that the dimensionality of the model of spatio-temporal chaos in our system can be drastically reduced.

Quantitative characterization of spatiotemporal chaos II: Dynamic aspects and anomalous scaling

Spatiotemporal chaos is characterized quantitatively. The characterization of a special model for coupled map lattices has been carried out successfully yet. The dynamic aspects of this model are discussed in the present paper. Anomalous scaling of the probability distribution function for the local Lyapunov exponent is shown. The characteristics of one model for spatiotemporal chaos are given statistically.

Spatiotemporal chaos in one- and two-dimensional coupled map lattices

Coupled map lattices are investigated as a model for spatiotemporal chaos. Pattern dynamics in diffusively coupled logistic lattice is briefly reviewed with the use of power spectra, domain distribution, and Lyapunov spectra. Mechanism of pattern selection with the suppression of chaos is discussed. Pattern dynamics on a 2-dimensional lattice is shown. In a weak coupling regime, a similarity with the one-dimensional case is found; frozen random pattern, selection, Brownian motion of a chaotic string, and intermittent collapse of the pattern with selective flicker noise. In a strong coupling regime, frozen pattern is found to be unstable by the surface tension, which is in contrast with the one-dimensional case. Convective coupling model is introduced in connection with the fluid turbulence of Navier-Stokes type. Soliton turbulence and vortex turbulence in the model are reported. Physical implications of coupled map lattices are discussed.