Four-dimensional System Research Articles

Image encryption scheme based on pseudo-DWT and cubic S-box

Combining a pseudo-Discrete Wavelet Transform (pseudo-DWT) and a novel cubic S-box technique, an image encryption scheme using a newly-developed four-dimensional hyperchaotic system (NewHS) is presented in this paper. The principal advantage of this method resides in its enhanced security, with hash values (computed by SHA-256) of the plaintext, thereby bolstering resistance to chosen-plaintext attack. Initially, a novel three-dimensional cubic S-box is designed via chaotic sequence, increasing the complexity and randomness. Subsequently, the proposed scheme employs a Ladder permutation for image scrambling, achieving a one-time pad encryption effect. Finally, a pseudo-DWT is devised to segment and reconstruct the image, implementing scrambling and diffusion encryption. Moreover, experiments and security analysis also prove that the proposed encryption scheme can show good performance.

A 4D conservative chaotic system: dynamics and realization

This paper proposes a novel four-dimensional conservative chaotic system (4D CCS) with a simple algebraic representation, comprising only two quadratic nonlinear terms. The dynamic characteristics of the 4D CCS are investigated by Poincaré mappings, Lyapunov exponents (LE), bifurcation diagrams, equilibrium points and spectral entropy (SE) complexity algorithm. Variations in parameters, initial values, and Hamiltonian energy lead to alternations between quasi-periodic and chaotic flows in the 4D CCS. The maximum Lyapunov exponent of the 4D CCS can reach a high value of 366300 under adjusting appropriate parameters and initial values. The pseudorandom sequences generated by the 4D CCS successfully pass the NIST test. Additionally, both the electronic circuit and FPGA implementation of the 4D CCS are carried out, with the experimental results aligning closely with the simulation results.

Nocturnal paroxysmal dystonia to sleep-related hypermotor epilepsy: A critical review.

Sleep-related paroxysmal motor episodes (SPMEs) have been described by various names, including nocturnal paroxysmal dystonia, nocturnal frontal lobe epilepsy (NFLE), and sleep-related hypermotor epilepsy. The underlying pathophysiology has been debated over the years, with these episodes assumed to be a form of paroxysmal dystonia or parasomnia versus a form of epilepsy. In most studies published on SPMEs and their variants (paroxysmal arousals, nocturnal paroxysmal dystonia, and episodic nocturnal wanderings) in the early 1990s, the authors speculated on the pathophysiology but did not commit to one idea. It was not until the mid-1990s that epilepsy became the leading prospect. We performed a narrative review of the major articles that have described this syndrome in a chronological fashion. We identified three eras, 1972-1993, 1994-1998, and 1999 to the present, each era marked by a landmark study. Our critical review of these early studies shows that the neurophysiological data supporting epilepsy as the sole basis for all SPME cases is very weak. In 1994-1995, a familial pattern of this syndrome was described and the term autosomal dominant NFLE was coined, with the authors claiming that all their patients had a form of frontal lobe epilepsy. With the exception of a few reference cases, the neurophysiological evidence that all patients had frontal lobe epilepsy was very weak. Compared to articles published on surgical series of frontal lobe epilepsy, the percentage of SPME cases with positive interictal/ictal electroencephalograms remained very low, seriously questioning the epileptic basis of the syndrome. Our critical review and analysis of the published literature shows that the evidence presented in favor of SPMEs being a homogenous focal epilepsy syndrome is very weak. Neurologists must recognize that SPMEs could be a form of movement disorder, parasomnia, or epilepsy. We recommend a pragmatic semiology-based classification of these episodes using the four-dimensional classification system.

Dynamics, periodic orbits of a novel four-dimensional hyperchaotic system with hidden attractors

In recent years, the investigation of systems featuring hidden attractors and coexisting attractors has garnered significant attention. This paper presents a novel four-dimensional (4D) hyperchaotic system devoid of equilibrium points, achieved by formulating an equation without a solution or constructing a system without fixed points. Due to the complex shape of this attractor, a novel coding method is utilized to establish symbol dynamics using eight letters. The proposed system exhibits highly intricate dynamics, including variations in topological structure with alterations in system parameters, as well as an exploration and discussion of four types of coexisting attractors. Our extensive practice has led us to propose a new conjecture: hyperchaotic systems with parameters close to the bifurcation point frequently display multistable states. Furthermore, the unstable periodic orbits with different topological lengths in the hidden hyperchaotic attractor are calculated systematically using the variational method. Additionally, the DSP circuit implementation is employed to validate the numerical simulation results for this new 4D system. Finally, adaptive synchronization is successfully realized within the system, thereby confirming its feasibility.

The design, circuit realization and applications of chaotic system with offset-boosting and multistability

Based on the foundation of a three-dimensional Jerk chaotic system, a novel four-dimensional chaotic system based on a memristor with cosine magneto-memristor is proposed. The system’s dynamical behavior is analyzed using bifurcation diagrams, Lyapunov exponents, multiple bifurcation diagrams, two-parameter Lyapunov exponents, complexity, and attractor basins. It is found that this new chaotic system exhibits characteristics such as multistability, transient chaos, intermittent chaos, spike discharge, controllable multi-vortex, and offset-boosting. The chaotic system is designed and simulated in analog circuit and realized in a digital circuit using a Field-Programmable Gate Array (FPGA). The consistency between simulation results and implementation results demonstrates the existence and feasibility of the system. Finally, the significance and superiority of the control scheme are verified based on the adaptive anti-synchronization control strategy, and the synchronization strategy is applied to image encryption, and the results show that the encryption effect is excellent and the anti-jamming ability is strong.

Exploring the dynamics of a four-dimensional Chua-like system: Numerical simulations and hardware investigations

In this work, we employ simulations to investigate deterministic and stochastic dynamics of a system governed by four coupled nonlinear ordinary differential equations (ODEs) derived from the canonical three-dimensional Chua model, replacing the piecewise nonlinearity with a cubic function. We employed two simulation approaches: (i) using software — where we performed numerical simulations (digital computation) in the ODEs model, and (ii) using hardware — where we performed experimental studies (analog computation) in the ODEs model. In the initial software-based approach for simulations, we performed stability and bifurcation analyses of the trivial equilibrium point, which were analytically conducted, along with the numerical continuation method. We solved the model using digital computation and explored its intricate dynamical behavior through nonlinear dynamics techniques applied to the parameter planes. In the second approach, employing hardware for simulations through analog computation, we designed an electronic circuit using analog electronics to solve the model in a continuous-time integration. The experimental setup mirrored the numerical simulations, yielding comparable results in terms of dynamical behaviors. This study underscores significant agreement between numerical and experimental findings, highlighting the robustness of the model across digital and analog contexts and offering practical insights into the various nonlinear dynamics presented in this system.

Enhanced 4D-OFDM optical communication systems with color-coded constellations and probability constellation shaping.

The present work introduces a four-dimensional probability constellation mapping OFDM optical transmission system based on a two-dimensional inverse fast Fourier transform (2D-IFFT). A four-dimensional constellation structure employing color coding is designed, amalgamating geometric shaping with probability shaping to enhance the constellation figure of merit (CFM). Successful transmission of OFDM signals at 51.49 Gb/s is achieved over a 2 km seven-core optical fiber, validating the performance of the proposed constellation diagram. Under the conditions of multicore multiplexing and a bit error rate of 3.8 × 10-3, the receiver sensitivity of the OFDM signals mapped with the proposed color-coded four-dimensional constellation exhibits gains of 0.8 dB, 1.33 dB, and 1.83 dB compared to traditional four-dimensional constellations, 3D-OFDM, and 2D-OFDM modulation, respectively. Furthermore, under an entropy value of 4.4 bits/symbol, a receiver sensitivity gain of 1.36 dB is attained compared to a uniform distribution constellation, indicating the favorable error performance of this scheme with promising prospects for short-distance communication in the future.

Jeffrey fluid saturating a heated porous layer: Dynamical and microcontroller execution probing

In this paper, a dynamical investigation and microcontroller execution on a Jeffrey fluid saturating a porous layer with bottom heating and periodic modulation of gravity is carried out. The continuity equation, the energy conservation equation and the Boussinesq-Darcy approximation are used to describe the Jeffrey fluid saturating a porous layer with bottom heating and periodic gravity modulation. Thanks to the truncated Galerkin expansion method, the partial differential equations obtained from the modelling is reduced to four first order ordinary differential equations. This four-dimensional system without gravity modulation has three or one steady states depending on the scaled thermal Rayleigh number and the non-dimensional ratio of relaxation time to the retardation time of the fluid. From the stability analysis of the obtained equilibrium points in the four-dimensional system without gravity modulation, it is revealed that the steady states are stable or unstable depending on the non-dimensional ratio of relaxation time to retardation time of the fluid. Without gravity modulation, the four-dimensional system experiences Hopf bifurcation, steady convection, periodic convections, seven different shapes of chaotic convections, bistable period-1-convection, bistable period-3-convections and coexisting convections. With the sinusoidal periodic gravity modulation, the four-dimensional system displays Hopf bifurcation, steady convections, periodic convections, bursting convections, quasiperiodic convections and three different shapes of chaotic convections. A microcontroller execution of the four-dimensional system is used to establish the convection characteristics spotted in the four-dimensional system without and with sinusoidal periodic gravity modulation during the numerical simulations.

A new four-dimensional memristive system, synchronization and its application in image encryption

A new four-dimensional memristive system, synchronization and its application in image encryption

Design and analysis of image encryption based on memristor chaotic systems with hidden attractors

Chaotic systems with hidden attractors are important research hotspots in nonlinear science. In recent years, continuous chaotic systems with special equilibrium points have been widely studied, especially continuous chaotic systems without equilibrium points. A four-dimensional chaotic system devoid of equilibrium point is proposed by using a composite cosine piecewise-linear (COS-PWL)function and a memristor model based on the modified Sprott-C system. The dynamical behaviors of the new system are studied through numerical analysis methods. The results reveal it is extremely sensitive to control parameters as well as initial conditions, which make it particularly suitable for application to image encryption algorithms. In light of these findings, a novel image encryption algorithm is introduced. This algorithm integrates the new four-dimensional chaotic system with ribonucleic acid (RNA) coding technology. Furthermore, the simulation results and security analyses validate the rationality of the encryption mechanism and the robustness of the encryption security of the proposed image encryption algorithm.

Cross-channel image encryption algorithm on the basis of a conservative hyperchaotic system

In image encryption, the traditional encryption means of scrambling and diffusion are widely used, but they fail to completely eliminate the correlation between the channels of the ciphertext image and still exist security risks. The selecting channel and position scrambling and cross-channel S-shaped diffusion methods proposed in this study push the encryption to a new depth. Compared with ordinary methods, it is more thorough in disrupting pixel positions, increases the complexity of pixel relationships between different channels, and substantially improves the unpredictability of encryption. To support this approach, we design a four-dimensional conservative hyperchaotic system with a very large hyperchaotic interval, which combines the high randomness of the conservative system and the broad key-space property of the hyperchaotic system, effectively defending against the risk of phase-space reconstruction aroused by missing attractors and reducing the possibility of being cracked. We deeply analyze the dynamic properties of the system by means of phase diagrams, bifurcation diagrams and Lyapunov exponents. The cross-channel scrambling and diffusion encryption algorithm designed based on this system not only ensures the security of image information during transmission, but also greatly enhances the ability to resist various attacks. The proposal of this method undoubtedly brings a secure solution to the field of image encryption.

Dynamics modeling of a memristor-based Rucklidge chaotic system: Multistability, offset boosting control and FPGA implementation

The complex dynamics greatly contributes to the application of chaos, especially the memristor chaotic systems that have emerged very recently. In this paper, a novel four-dimensional continuous chaotic system is developed by introducing a generalized memristor model into the classical Rucklidge system, and the rich dynamical traits are confirmed by theories and numerical simulations. System Hamilton energy is deduced and analyzed to expose the underlying energy evolution and chaos mechanism. And then, realizing the offset boosting control of the system promotes its engineering applications. Numerical simulations verify that the offset boosting controller can directly change the polarity of the chaotic signal. Specifically, bifurcation diagram, Lyapunov spectra, system complexity evolution diagram and dynamic evolution map are adopted to expound the rich dynamics. Meanwhile, the extreme multi-stability with various initial values resulting in an infinite number of coexisting attractors is also revealed. Finally, the proposed attractor is implemented using the Field Programmable Gate Array (FPGA) platform and building analog circuit based on Multisim. Among which, the former is potentially used to design the Pseudo-random signal generator in information encryption, while the latter is for verifying the existence of the proposed chaotic system.

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications.

Globally Exponentially Attracting Sets and Heteroclinic Orbits Revealed

Motivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov functions. Specifically, not only is a family of mathematical expressions of globally exponentially attracting sets derived, but the existence of a pair of orbits heteroclinic to S0 and S± is also proven with the aid of a Lyapunov function and the definitions of both the α-limit set and ω-limit set. Moreover, numerical examples are used to justify the theoretical analysis. Since the obtained results improve and complement the existing ones, they may provide support in chaos control, chaos synchronization, the Hausdorff and Lyapunov dimensions of strange attractors, etc.

Backstepping synchronization control for four-dimensional chaotic system based on DNA strand displacement

Backstepping control is an important nonlinear control design method, which realizes the control of complex systems by constructing control law step by step, and has significant advantages for dealing with complex nonlinear systems. This article proposes a synchronization technique for four-dimensional chaotic systems using a combination of backstepping control method and DNA strand displacement technology. By relying on theoretical knowledge of DNA molecules, five basic chemical reaction modules such as trigger reaction, reference reaction, catalytic reaction, annihilation reaction and degradation reaction are given to construct a four-dimensional DNA chaotic system. On the basis of the relevant theory of chaotic dynamics, the constructed system is analyzed by Lyapunov exponent diagram and spectral entropy complexity algorithm, and the results come to the conclusion that the system reveals extremely complex and varied dynamic behaviors. Combining DNA strand displacement technology with backstepping control method, four controllers are developed to ensure that the trajectories of two homogeneous chaotic systems are synchronized. The numerical simulation results validate the feasibility and applicability of the proposed method. The method proposed in this paper may provide some references in the field of DNA molecular chaos synchronization control.

The Construction of Learning Support Parameters for Adults with Autism

ABSTRACT Existing literature suggests adults with autism may only have limited access to support, which may fail to meet their diversified learning needs. This study thus aims to propose dimensions and parameters of a learning support system for adults with autism by means of focus group interviews (N = 30). The content analysis of interview data produced a four-dimensional learning support system for adults with autism: supporters, learners, learning resources, and learning environments. The supporter dimension was composed of four parameters, namely government support, social support, teacher support, and parental support. The learner dimension had two parameters, including satisfying interests and improving ability. The learning resources dimension comprised two parameters, involving learning aids and curriculum support. The learning environment dimension included two parameters, containing physical environment support and social-emotional environment support. The learning support system could be used as a benchmark for the development of adults with autism spectrum disorder. With parameters of learning support for adults with autism, this study is expected to provide guidance and reference for work and related research on learning support for adults with autism, so that their learning needs can be addressed and employment can be improved.

A Concise 4D Conservative Chaotic System with Wide Parameter Range, Offset Boosting Behavior and High Initial Sensitivity

In this paper, we present a concise four-dimensional (4D) conservative chaotic system with a wide parameter range. Since there are no terms higher than first order, the circuit does not contain multipliers, resulting in a simple circuit implementation. The nonlinear dynamic characteristics, such as phase diagrams, equilibrium points, divergence, Poincaré cross-sections, Lyapunov exponents, bifurcation diagrams, and Lyapunov dimension, are analyzed in detail, which illustrates the conservativity. Besides, the system exhibits different offset boosting behaviors. Through offset boosting, the system can propagate along a line, convert signal polarity, control variable amplitude, generate coexisting attractors, and even induce changes in its state. Specially, we realize the transition from a single-vortex attractor to a multivortex one by some changes in the initial values. Furthermore, the Pearson correlation coefficient is used to demonstrate the higher initial value sensitivity of the system. Finally, the system is implemented through Multisim simulation and analog circuit separately, and their consistency validates the system effectively.

O01 Mapping the cellular and molecular dynamics of mouse and human hair follicles reveals mechanisms of hair growth

Abstract Introduction and aims Tissue homeostasis in continuously renewing organs, such as the skin, rely on orchestrated cellular and molecular dynamics. The hair follicle (HF) is characterized by distinct keratinocytes organized in transcriptionally and functionally distinct concentric HF layers. The anagen progenitor cells (also called germinative layer cells) are located juxtaposed to the dermal papilla and give rise to each of the differentiated layers. Despite this well-known high level of organization and cell-lineage separation, it is still unclear how the germinative layer cells coordinate hair growth and commit to specific lineages. Methods Here, we employed single-cell RNA sequencing, single-molecule mRNA fluorescence in situ hybridization and in vivo lineage tracing to show how the matrix progenitor cells commit and contribute to the HF lineages depending on their position. Furthermore, we developed a four-dimensional live imaging system of the human HF to construct a global map of single-cell dynamics. Results We show that the HF progenitors dynamically relocate in a conveyor-belt-like movement, switch their lineage fate and gradually restrict their potential. This spatiotemporal cell choreography is characterized by a gradual change of expression from Lgr5 in the lower proximal cup, through Dcn, Id3 and Msx1 in the central part, to distal Lef1 expression where the medulla lineage starts. Detailed in situ mRNA staining and mouse clonal lineage tracing show the transcriptional changes and gradual lineage restriction of matrix progenitors in the spatial context. Combining human HF imaging with fluid dynamics theories, we uncovered a spiral-like downward movement of outer root sheath cells, feeding the germinative layer stem cells, and revealed a pulling force induced by the outer root sheath cells as a critical driver for hair growth. Conclusions Taken together, our study uncovered how HF progenitor cells progress in a conveyor-belt-like manner through several transcriptional states and discovered new cellular and molecular mechanisms regulating hair formation.

Analysis of a time-dependent memristor-based chaotic system and its application in image encryption

Abstract Compared with ordinary chaotic systems, memristor-based chaotic systems have more complex dynamic behaviors and are more suitable for image encryption algorithms. In this paper, a four-dimensional chaotic system is constructed by introducing a cubic nonlinear memristor into a three-dimensional chaotic system. Firstly, the dynamic characteristics of the constructed memristor-based chaotic system are analyzed in detail, and the simulation results show that the system has different attractors with different topological structures at different simulation times. Within a fixed simulation time, the system has 15 attractors with different topological structures under different parameter values, and there is a phenomenon of multiple stability in the system, indicating high complexity. Based on the above discoveries, a color image encryption algorithm including scrambling and diffusion is designed. Experimental results show that this algorithm can perfectly hide the information of the plaintext image, and the decrypted image is consistent with the plaintext image. Finally, the security of the algorithm is analyzed by using key space and so on. The analysis results indicate that the encryption algorithm designed in this paper can effectively resist external attacks and has high security.

Ultra-high-speed four-dimensional hyperspectral imaging

We propose, to the best of our knowledge, a novel deep learning–enabled four-dimensional spectral imaging system composed of a reflective coded aperture snapshot spectral imaging system and a panchromatic camera. The system simultaneously captures a compressively coded hyperspectral measurement and a panchromatic measurement. The hyperspectral data cube is recovered by the U-net-3D network. The depth information of the scene is then acquired by estimating a disparity map between the hyperspectral data cube and the panchromatic measurement through stereo matching. This disparity map is used to align the hyperspectral data cube and the panchromatic measurement. A designed fusion network is used to improve the spatial reconstruction of the hyperspectral data cube by fusing aligned panchromatic measurements. The hardware prototype of the proposed system demonstrates high-speed four-dimensional spectral imaging that allows for simultaneously acquiring depth and spectral images with an 8 nm spectral resolution between 450 and 700 nm, 2.5 mm depth accuracy, and a 1.83 s reconstruction time.