Three-Wave Mixing of Dipole Solitons in One-Dimensional Quasi-Phase-Matched Nonlinear Crystals

A quasi-phase-matched technique is introduced for soliton transmission in a quadratic[χ^((2))]nonlinear crystal to realize the stable transmission of dipole solitons in a one-dimensional space under three-wave mixing.We report four types of solitons as dipole solitons with distances between their bimodal peaks that can be laid out in different stripes.We study three cases of these solitons:spaced three stripes apart,one stripe apart,and confined to the same stripe.For the case of three stripes apart,all four types have stable results,but for the case of one stripe apart,stable solutions can only be found atω_(1)=ω_(2),and for the condition of dipole solitons confined to one stripe,stable solutions exist only for Type1 and Type3 atω_(1)=ω_(2).The stability of the soliton solution is solved and verified using the imaginary time propagation method and real-time transfer propagation,and soliton solutions are shown to exist in the multistability case.In addition,the relations of the transportation characteristics of the dipole soliton and the modulation parameters are numerically investigated.Finally,possible approaches for the experimental realization of the solitons are outlined.

Chaotic CS Encryption:An Efficient Image Encryption Algorithm Based on Chebyshev Chaotic System and Compressive Sensing

Images are the most important carrier of human information. Moreover, how to safely transmit digital imagesthrough public channels has become an urgent problem. In this paper, we propose a novel image encryptionalgorithm, called chaotic compressive sensing (CS) encryption (CCSE), which can not only improve the efficiencyof image transmission but also introduce the high security of the chaotic system. Specifically, the proposed CCSEcan fully leverage the advantages of the Chebyshev chaotic system and CS, enabling it to withstand various attacks,such as differential attacks, and exhibit robustness. First, we use a sparse trans-form to sparse the plaintext imageand then use theArnold transformto perturb the image pixels. After that,we elaborate aChebyshev Toeplitz chaoticsensing matrix for CCSE. By using this Toeplitz matrix, the perturbed image is compressed and sampled to reducethe transmission bandwidth and the amount of data. Finally, a bilateral diffusion operator and a chaotic encryptionoperator are used to perturb and expand the image pixels to change the pixel position and value of the compressedimage, and ultimately obtain an encrypted image. Experimental results show that our method can be resistant tovarious attacks, such as the statistical attack and noise attack, and can outperform its current competitors.

Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities.

Chaotic Map-Based Authentication and Key Agreement Protocol with Low-Latency for Metasystem

With the rapid advancement in exploring perceptual interactions and digital twins,metaverse technology has emerged to transcend the constraints of space-time and reality,facilitating remote AI-based collaboration.In this dynamic metasystem environment,frequent information exchanges necessitate robust security measures,with Authentication and Key Agreement(AKA)serving as the primary line of defense to ensure communication security.However,traditional AKA protocols fall short in meeting the low-latency requirements essential for synchronous interactions within the metaverse.To address this challenge and enable nearly latency-free interactions,a novel low-latency AKA protocol based on chaotic maps is proposed.This protocol not only ensures mutual authentication of entities within the metasystem but also generates secure session keys.The security of these session keys is rigorously validated through formal proofs,formal verification,and informal proofs.When confronted with the Dolev-Yao(DY)threat model,the session keys are formally demonstrated to be secure under the Real-or-Random(ROR)model.The proposed protocol is further validated through simulations conducted using VMware workstation compiled in HLPSL language and C language.The simulation results affirm the protocol’s effectiveness in resisting well-known attacks while achieving the desired low latency for optimal metaverse interactions.

CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction

To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR.

Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.

A color image encryption scheme based on a 2D coupled chaotic system and diagonal scrambling algorithm

A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.

A chaotic hierarchical encryption/watermark embedding scheme for multi-medical images based on row-column confusion and closed-loop bi-directional diffusion

Security during remote transmission has been an important concern for researchers in recent years.In this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is designed,and a multiimage encryption(MIE)algorithm with row and column confusion and closed-loop bi-directional diffusion is adopted in the paper.While ensuring secure communication of medical image information,people with different security levels have different levels of decryption keys,and differentiated visual effects can be obtained by using the strong sensitivity of chaotic keys.The highest security level can obtain decrypted images without watermarks,and at the same time,patient information and copyright attribution can be verified by obtaining watermark images.The experimental results show that the scheme is sufficiently secure as an MIE scheme with visualized differences and the encryption and decryption efficiency is significantly improved compared to other works.

Intrusion Detection Model Using Chaotic MAP for Network Coding Enabled Mobile Small Cells

Wireless Network security management is difficult because of the ever-increasing number of wireless network malfunctions,vulnerabilities,and assaults.Complex security systems,such as Intrusion Detection Systems(IDS),are essential due to the limitations of simpler security measures,such as cryptography and firewalls.Due to their compact nature and low energy reserves,wireless networks present a significant challenge for security procedures.The features of small cells can cause threats to the network.Network Coding(NC)enabled small cells are vulnerable to various types of attacks.Avoiding attacks and performing secure“peer”to“peer”data transmission is a challenging task in small cells.Due to the low power and memory requirements of the proposed model,it is well suited to use with constrained small cells.An attacker cannot change the contents of data and generate a new Hashed Homomorphic Message Authentication Code(HHMAC)hash between transmissions since the HMAC function is generated using the shared secret.In this research,a chaotic sequence mapping based low overhead 1D Improved Logistic Map is used to secure“peer”to“peer”data transmission model using lightweight H-MAC(1D-LM-P2P-LHHMAC)is proposed with accurate intrusion detection.The proposed model is evaluated with the traditional models by considering various evaluation metrics like Vector Set Generation Accuracy Levels,Key Pair Generation Time Levels,Chaotic Map Accuracy Levels,Intrusion Detection Accuracy Levels,and the results represent that the proposed model performance in chaotic map accuracy level is 98%and intrusion detection is 98.2%.The proposed model is compared with the traditional models and the results represent that the proposed model secure data transmission levels are high.

Distributional Chaoticity of the Minimal Subshift of Shift Operators

This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.

High-Order Solitons and Hybrid Behavior of (3 + 1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation with Variable Coefficients

In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions.

Annihilation Solitons and Chaotic Solitons for the （2＋1）-Dimensional Breaking Soliton System

By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.

An Approach for the Construction of Systems That Self-Generate Chaotic Solitons

This paper proposes a method for constructing partial differential equation (PDE) systems with chaotic solitons by using truncated normal forms of an ordinary differential equation (ODE). The construction is based mainly on the fact that the existence of a soliton in a PDE system is equal to that of a homoclinic orbit in a related ODE system, and that chaos of ?i’lnikov homoclinic type in the ODE imply that the soliton in the PDE changes its profile chaotically along propagation direction. It is guaranteed that the constructed systems can self-generate chaotic solitons without any external perturbation but with constrained wave velocities in a rigorously mathematical sense.

Chaotic Solitons in Deoxyribonucleic Acid (DNA) Interacting with a Plane Wave

Theoretical analysis of the DNA dynamics reveals that interaction between the single solitons and plane wave implies Smale-horseshoe chaos in the double helices. Solutions of the chaotic solitons are derived from a direct perturbation technique. It is demonstrated that to produce the bounded chaotic solitons, velocities of the solit ons nust be the same and equal to propagation velocity of the plane wave in DNA. The result shows that the DNA structure may be destroyed by the long action of an electromagnetic wave. It also supplies a useful method for controlling the velocities and unboundedness of the DNA motion in a tumour cell by using a plane wave.

A Chaotic Local Search-Based Particle Swarm Optimizer for Large-Scale Complex Wind Farm Layout Optimization

Wind energy has been widely applied in power generation to alleviate climate problems.The wind turbine layout of a wind farm is a primary factor of impacting power conversion efficiency due to the wake effect that reduces the power outputs of wind turbines located in downstream.Wind farm layout optimization(WFLO)aims to reduce the wake effect for maximizing the power outputs of the wind farm.Nevertheless,the wake effect among wind turbines increases significantly as the number of wind turbines increases in the wind farm,which severely affect power conversion efficiency.Conventional heuristic algorithms suffer from issues of low solution quality and local optimum for large-scale WFLO under complex wind scenarios.Thus,a chaotic local search-based genetic learning particle swarm optimizer(CGPSO)is proposed to optimize large-scale WFLO problems.CGPSO is tested on four larger-scale wind farms under four complex wind scenarios and compares with eight state-of-the-art algorithms.The experiment results indicate that CGPSO significantly outperforms its competitors in terms of performance,stability,and robustness.To be specific,a success and failure memories-based selection is proposed to choose a chaotic map for chaotic search local.It improves the solution quality.The parameter and search pattern of chaotic local search are also analyzed for WFLO problems.

Securing 3D Point and Mesh Fog Data Using Novel Chaotic Cat Map

With the rapid evolution of Internet technology,fog computing has taken a major role in managing large amounts of data.The major concerns in this domain are security and privacy.Therefore,attaining a reliable level of confidentiality in the fog computing environment is a pivotal task.Among different types of data stored in the fog,the 3D point and mesh fog data are increasingly popular in recent days,due to the growth of 3D modelling and 3D printing technologies.Hence,in this research,we propose a novel scheme for preserving the privacy of 3D point and mesh fog data.Chaotic Cat mapbased data encryption is a recently trending research area due to its unique properties like pseudo-randomness,deterministic nature,sensitivity to initial conditions,ergodicity,etc.To boost encryption efficiency significantly,in this work,we propose a novel Chaotic Cat map.The sequence generated by this map is used to transform the coordinates of the fog data.The improved range of the proposed map is depicted using bifurcation analysis.The quality of the proposed Chaotic Cat map is also analyzed using metrics like Lyapunov exponent and approximate entropy.We also demonstrate the performance of the proposed encryption framework using attacks like brute-force attack and statistical attack.The experimental results clearly depict that the proposed framework produces the best results compared to the previous works in the literature.

High-order effect on the transmission of two optical solitons

For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers,a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is needed.In this paper,in order to study the dynamic mechanism of femtosecond solitons in different media,we take the nonlinear Schr?dinger equation considering higher-order effects as the theoretical model,discuss the propagation of solitons in single-mode fibers,and explore the third-order dispersion and third-order nonlinear effects on the generation of optical solitons.The exact solution of the theoretical model is obtained through the bilinear method,and the transmission characteristics of two solitons with exact soliton solutions in actual fiber systems are analyzed and studied.The influence of various conditions on the transmission and interaction of optical solitons is explored.Methods for optimizing the transmission characteristics of optical solitons in optical communication systems are suggested.The relevant conclusions of this paper have guiding significance for improving the quality of fiber optic communication and increasing bit rates.

Special breathing structures induced by bright solitons collision in a binary dipolar Bose–Einstein condensates

We numerically investigate the breathing dynamics induced by collision between bright solitons in a binary dipolar Bose–Einstein condensates, whose dipole–dipole interaction and contact interaction are attractive. We identify three special breathing structures, such as snakelike special breathing structure, mixed breathing structure, and divide breathing structure.The characteristics of these breathing structures can be described by breathing frequency ?, maximum breathing amplitude A and lifetime τ, which can be manipulated by atomic number Ni and interspecies scattering length a12. Meanwhile, the above breathing structures can realize the process of quasi-transition with a reasonable Ni and a12. Additionally, the collision of two special breathing structures also can bring more abundant breathing dynamics. Our results provide a reference for the study of soliton interactions and deepen the understanding of soliton properties in a binary dipolar Bose–Einstein condensates.

Two-Dimensional Gap Solitons in Parity-Time Symmetry Moiré Optical Lattices with Rydberg–Rydberg Interaction

Realizing single light solitons that are stable in high dimensions is a long-standing goal in research of nonlinear optical physics.Here,we address a scheme to generate stable two-dimensional solitons in a cold Rydberg atomic system with a parity-time(PT) symmetric moiré optical lattice.We uncover the formation,properties,and their dynamics of fundamental and two-pole gap solitons as well as vortical ones.The PT symmetry,lattice strength,and the degrees of local and nonlocal nonlinearity are tunable and can be used to control solitons.The stability regions of these solitons are evaluated in two numerical ways:linear-stability analysis and time evolutions with perturbations.Our results provide an insightful understanding of solitons physics in combined versatile platforms of PT-symmetric systems and Rydberg–Rydberg interaction in cold gases.

Quantum Squeezing of Matter-Wave Solitons in Bose-Einstein Condensates

We investigate the quantum squeezing of matter-wave solitons in atomic Bose-Einstein condensates.By calculating quantum fluctuations of the solitons via solving the Bogoliubov-de Gennes equations,we show that significant quantum squeezing can be realized for both bright and dark solitons.We also show that the squeezing efficiency of the solitons can be enhanced and manipulated by atom-atom interaction and soliton blackness.The results reported here are beneficial not only for understanding quantum property of matter-wave solitons,but also for promising applications of Bose-condensed quantum gases.