Four-dimensional System Research Articles

A (4, 4) threshold protocol of semi-quantum secret sharing using entangled state

Abstract Quantum secret sharing (QSS) can address the increasing threat of computing power. While semi-QSS protocols alleviate participants’ reliance on quantum devices, ensuring security and lowering the participation difficulty. In this paper, we propose a semi-QSS protocol based on four quantum entangled states within a four-dimensional quantum system. It generates a four-dimensional four-quantum entangled state through a dealer, requiring full quantum capability for the dealer and only partial quantum capability for the participants. Participants perform random operations on the received qubits, and eavesdropping detection is based on these random operations. Then the dealer can choose the correct measurement basis based on the receiver’s specific operations. The security and quantum efficiency of protocol depend on the ratio of information to decoy particles inserted by the dealer. Furthermore, the security analysis shows that the protocol is resistant to common quantum attacks.

A new color image encryption scheme based on DNA sequence operations and novel hyper-chaotic system

Abstract Aiming at the problems of weak key sensitivity and small key space of
image encryption algorithm,in this paper,we propose an image encryption algorithm
based on four-dimensional memristive hyperchaotic system and DNA operation. The
algorithm first calculates the initial value of the image information by Secure Hash
Algorithm 512(SHA-512) hash algorithm, substitutes it into the four-dimensional
memory-damped hyperchaotic system to generate a sequence, and then obtains the key
map by Logistic mapping and Sine mapping.The preprocessed image matrix is obtained
by dot-multiplication operation of the plaintext image with the square matrix generated
by Sigmoid algorithm after Arnold permutation.Then DNA encoding,DNA row-by-
row operation and DNA decoding are performed on the key map and preprocessed
image, and at the end, the encrypted image is obtained after rotating the first round
encrypted image and the key map by 90° for the second encryption.Experiments such as
robustness analysis,anti-differential attack,and adjacent pixel correlation analysis show
that the algorithm has a large key space,strong key sensitivity and the encrypted image
has a small adjacent pixel correlation.It is shown that the algorithm can effectively
protect the communication encryption of digital images.

Design, analysis and application of Non-Hamiltonian conservative chaotic system based on memristor

A new four-dimensional memristor conservative chaotic system (MCCS) is constructed by introducing a sine magnetic memristor into the Sprott-A system in this paper. Through the analysis of the dynamic behavior of the MCCS, it is found that the system is a non-Hamiltonian chaotic system, exhibiting continuous chaotic intervals and high complexity. At the same time, a series of special phenomena have been observed in MCCS, such as multiple stability, parameter-controllable multi-scrolls, bursty oscillations, and distinctive spike oscillations. Additionally, the correctness of the mathematical model of the MCCS is confirmed through analog and FPGA digital circuit. Finally, a synchronous encryption system with strong attack resistance is designed by combining MCCS with RNA algorithm.

Initial-offset and amplitude control of multi-scroll attractor in a chaotic jerk system

Abstract With the gradual deepening of research on chaos, in order to flexibly apply chaos, offset boosting and amplitude control have become a hot topic. However, few people have studied chaotic systems with multi-scroll attractor under initial conditions.
This paper constructs and analyzes a simple four-dimensional chaotic system. Unlike other extension methods that modify the original seed system, this method does not make any changes to the original seed system, only adds a new variable in the extension dimension. It is found that the proposed system can achieve offset boosting and amplitude control by changing the initial values, and the system has characteristics such as multi-scroll attractors, infinite equilibrium points, symmetry, and so on. Finally, FPGA hardware implementation was carried out to verify the numerical results.

Optimizing Security and Cost Efficiency in N-Level Cascaded Chaotic-Based Secure Communication System

In recent years, chaos-based secure communication systems have garnered significant attention for their unique attributes, including sensitivity to initial conditions and periodic orbit density. However, existing systems face challenges in balancing encryption strength with practical implementation, especially for multiple levels. This paper addresses this gap by introducing a novel N-level cascaded chaotic-based secure communication system for voice encryption, leveraging the four-dimensional unified hyperchaotic system. Performance evaluation is conducted using various security metrics, including Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR), Percent Residual Deviation (PRD), and correlation coefficient, as well as Field-Programmable Gate Array (FPGA) resource metrics. A new Value-Based Performance Metrics (VBPM) framework is also introduced, focusing on both security and efficiency. Simulation results reveal that the system achieves optimal performance at N = 4 levels, demonstrating significant improvements in both security and FPGA resource utilization compared to existing approaches. This research offers a scalable and cost-efficient solution for secure communication systems, with broader implications for real-time encryption in practical applications.

Multi-wing chaotic system based on meminductor and its application in image encryption

Meminductor is a novel type of nonlinear device following the memristor, characterized by its memory properties. Currently, research on meminductors is still in its infancy, with their physical devices yet to be formally realized. Therefore, conducting fundamental research on their nonlinear circuit properties and applications is of great significance. In this paper, a new multi-wing chaotic system is proposed based on the mathematical model of a magnetically controlled meminductor. By varying the values of its parameters, the system can generate two-wing, three-wing, and four-wing chaotic attractors. Various analytical methods are employed to study the dynamical behaviours of the proposed chaotic system. The results demonstrate that the system is highly sensitive to its initial conditions and control parameters, which makes it suitable for image encryption. Based on the new system, we propose a new algorithm for image encryption that combines the newly established four-dimensional multi-wing chaotic system with bit plane decomposition technique, firstly, the high four-bit planes containing 94% image information are disordered by S-type permutation, then the disordered bit planes perform operation of XOR with the random matrix generated by chaotic sequences, and finally, the encrypted image is obtained by merging the bit planes.

A color image encryption algorithm based on a novel 4D hyperchaotic system and bit-level diffusion

As digital images are widely used in social media, medical, military and other fields, ensuring the privacy and security of image data has become a critical concern. Firstly, we propose a novel four-dimensional hyperchaotic system and validate that it exhibits a broad chaotic range, as demonstrated by bifurcation diagrams and Lyapunov exponent experiments. Additionally, simulated circuit diagrams verify the hardware feasibility of the proposed system. Secondly, we design a dynamic iterative scrambling (DIS) scheme that dynamically divides the image into multiple matrices for spatially indexed scrambling. Excellent substitution performance can be ensured by multiple iterations. In the diffusion stage, a multidirectional bit-level L-shaped (MDBL) scheme is proposed. Diffusion is conducted on the bit plane using a designed cross-multiplanar selection algorithm, which fuses the high and low bit planes, thereby enhancing the diffusion performance of MDBL. Thirdly, Based on the above concepts, a novel four-dimensional hyperchaotic system and an encryption algorithm based on bit-level diffusion are proposed. Finally, experimental results and security analyses demonstrate the effectiveness of the novel 4D hyperchaotic system and image encryption scheme. The proposed encryption scheme exhibits robust anti-interference capabilities and effectively safeguards image security.

Ocean data assimilation focusing on integral quantities characterizing observation profiles

An observation operator in data assimilation was formalized based on the signatures extracted from the integral quantities contained within observed vertical profiles in the ocean. A four-dimensional variational global ocean data assimilation system, founded on this observation operator, was developed and utilized to conduct preliminary data assimilation experiments over a ten-year assimilation window, comparing the proposed method, namely profile-by-profile matching, with the traditional method, namely point-by-point matching. The proposed method not only demonstrated a point-by-point skill comparable to the traditional method but also provided superior analysis fields in terms of profile shapes on the temperature-salinity plane. This is an indication of a well-balanced analysis field, in contrast to the traditional method, which can produce extremely poor relative errors for certain metrics. Additionally, signatures were shown to successfully represent properties of the water column, such as steric height, and serve as an effective new diagnostic tool. The top-down, or macro–micro, viewpoint in this method is fundamental to the extent that it can offer an alternative view of how we comprehend ocean observations, holding significant implications for the advancement of data assimilation.

A Communication Research on Reshaping the Content Ecosystem of New Media Platforms Based on AIGC Technology

In the era of omnimedia, the rapid development of Artificial Intelligence Generated Content (AIGC) technology has profoundly and extensively influenced the news and public opinion ecosystem. This paper delves into how mainstream media utilize AIGC technology to reshape their agenda-setting capabilities within the context of intelligent communication, and exhaustively explores the specific applications of this technology on new media platforms and their resulting communication effects. Through systematic analysis, the study finds that mainstream media, empowered by intelligent communication technology, have successfully constructed a four-dimensional support system centered on discourse interpretation, discourse connectivity, discourse affinity, and discourse guidance. This system not only strengthens the discourse power and influence of mainstream media on new media platforms but also promotes the formation of a new mainstream opinion landscape, providing robust support for constructing a healthy and orderly news and public opinion ecosystem. Specifically, mainstream media utilize AIGC technology to enhance the efficiency and quality of content production, achieve precise content delivery and personalized communication, and effectively strengthen interaction and connection with audiences. Meanwhile, by reinforcing discourse interpretation and guidance, mainstream media maintain a clear orientation in the complex and ever-changing public opinion environment. The application of AIGC technology injects new vitality into the development of mainstream media in the new media era and provides essential impetus for the continuous optimization of the news and public opinion ecosystem.

Influencing Factors of Sustainable Rural Entrepreneurship: A Four-Dimensional Evaluation System Encompassing Entrepreneurs, Economy, Society, and Environment

The implementation of rural entrepreneurship emerges as a pivotal pathway for fostering rural economic growth. However, unsustainable entrepreneurial endeavors have posed notable ecological threats and environmental degradation. Drawing upon the triple bottom line framework, this research devised a comprehensive evaluation system for sustainable rural entrepreneurship, spanning four dimensions: entrepreneurs, economic, social, and environmental aspects. Employing the fuzzy Decision-Making Trial and Evaluation Laboratory (DANP) approach, we delineated the intricate causal relationships among influencing factors and identified key determinants along with their respective weights. Our findings underscore the prominence of economic dimensions in fostering sustainable rural entrepreneurship. Specifically, entrepreneurial motivation, type of entrepreneurship, financial backing, economic value, favorable policy frameworks, and a conducive business environment emerged as pivotal indicators. Notably, the type of entrepreneurship, financial support, economic value, and favorable policies emerged as propelling factors driving sustainable rural entrepreneurial progress. Conversely, entrepreneurial motivation and the business environment manifested as dependent factors within this causal nexus. This study offers valuable managerial implications for entrepreneurial teams and pertinent government agencies, enabling decision-makers to formulate evidence-based strategies aimed at realizing sustainable rural entrepreneurship.

Analysis of stability and bifurcation and design of optimal control for phytoplankton–zooplankton–fish model with additional food and fish harvesting

ABSTRACT This paper investigates the dynamics of a four-dimensional plankton-fish system that contains three communities of plankton: non-toxic phytoplankton, toxic-producing phytoplankton, and zooplankton. The zooplankton consumes both non-toxic and toxic-producing phytoplankton. First, the positivity and boundedness of the solutions in the plankton-fish model are evaluated. Then, we derive the conditions for the existence of ecologically possible equilibria and their local and global asymptotic nature. Furthermore, we evaluate the criteria for the existence of Hopf-bifurcation and transcritical bifurcation. By applying Pontryagin’s maximum principle, we investigate the optimal control of fish harvesting, where fishing effort is taken as a control parameter. By using phase-space diagrams, time responses, bifurcation diagrams, and numerical analyses validate the theoretical results. The numerical results including maximum Lyapunov exponent verify chaotic dynamics of the system. We notice that a suitable choice of harvesting, phytoplankton growth rate, and additional food parameters can control the chaotic behavior of the presented model. The proposed novel mathematical model gives deeper insights to theoretical ecologists on how toxic-producing phytoplankton affects zooplankton and fish populations in aquatic systems. Furthermore, the proposed model is more appropriate for fish harvesting to maximize profit as well as species conversion in the presence of toxic phytoplankton.

Encryption algorithm based on improved four-dimensional chaotic system and dynamic DNA encoding

An image encryption algorithm is proposed based on the combination of genetic (DNA) random coding and chaotic mapping. An image encryption algorithm based on an improved new four-dimensional chaotic system and DNA coding is proposed to address the problem that a single coding method is prone to selecting plaintext attacks. Based on a four-dimensional chaotic system existing in the literature, a new four-dimensional hyperchaotic system is obtained through improvement. The initial value of the system is generated based on SHA-256, zigzag transform. The input key and four pseudo-random chaotic sequences are generated iteratively. DNA chunking encoding, arithmetic operation, and decoding are implemented for the image disrupted based on the zigzag transform. The two-dimensional matrix constituted based on the Chaotic Sequence of Chebyshev to obtain the scrambled and diffused ciphertext image. Simulation experiments and security performance analysis show that the algorithm enhances the correlation between the key and the plaintext, the randomness of the encryption process, and effectively improves the anti-attack capability [H. Chen, J. Zhao et al., Appl. Res. Comput. 10, 0434 (2021)]. In this paper, 512 × 512 × 3 peppers color images are used for testing, and the correlation coefficients of adjacent pixels of the encrypted images are all close to 0, and the information entropy is all more significant than 7.997, which is relative to the theoretical value of 8. The experimental results show that the proposed algorithm improves the security of the ciphertext, increases the critical space, and, at the same time, resists various attack methods.

Evolution characteristics and mechanism of meso-γ-scale vortex in an atypical bow echo in the North China Plain

On June 25, 2020, an atypical bow echo (ATBE) accompanied by a meso-γ-scale vortex (MV) incurred the strongest gust (41.4 m s−1) recorded since 1957 in the North China Plain. In this article, we investigate the evolution characteristics of MV and its mechanism for the extreme wind by using the observation data of Doppler weather radar and automatic weather stations as well as the four-dimensional Variational Doppler Radar Analysis System (VDRAS). The results show that the MV in this process was initially born at a height of 0.9–2.4 km, and the contracting and stretching vertical vortex rapidly descended to surface from the 2.0 km height with the rotation speed increasing rapidly. Six minutes later, the extreme wind occurred. The generation mechanism of the MV is that, under the strong vertical wind shear and downdraft in the lower troposphere, the vertical vortex tube of MV was transformed from the horizontal vortex tube generated in the zone of perturbation temperature gradient. The influence mechanism of MV on the extreme wind is that, as the MV continued to intensify and extend downward, a negative perturbation low-pressure center formed in the lower troposphere near the MV. Meanwhile, the descending rear-inflow jet (RIJ) was blocked by the prefrontal upward motion and a positive perturbation high-pressure center formed at around 1 km height. The violent positive-negative couplets of perturbation pressure gradient produced a downward nonhydrostatic perturbation pressure gradient force (NPPGF) that further intensified the vertical downward velocity. In addition to the strong downdraft velocity, the Coriolis force also enhanced the formation of the extreme wind through the action of ageostrophic winds. Besides, this paper also compares the mechanism of this process with that of a typical bow echo MV and the extreme wind it affected.

A Four-Dimensional No-Equilibrium Chaotic System with Multi-Scroll Chaotic Hidden Attractors and its Application in Image Encryption

Abstract In recent years, constructing hidden attractors with multi-scroll has become a key discussion point in the research and application fields of chaos science. In this paper, with the existing four-dimensional (4D) chaotic system as the base, a new four-dimensional chaotic system featuring significant characteristics of multi-scroll hidden attractors is constructed by adding a nonlinear function. Comprehensive studies including theoretical analyses and numerical simulations have been carried out on the dynamic properties of the new chaotic system, and all the results show that this system exhibits extremely complex chaotic behaviours and excellent unpredictability, which has great value in image encryption. Therefore, an image encryption scheme based on the new chaotic system is proposed, which cleverly integrates the new scrambling algorithm based on parity coordinate transformation and the new rotational diffusion algorithm. And the effectiveness of this encryption algorithm has been thoroughly analyzed and tested. The results based on the experiments show that this encryption algorithm exhibits significant advantages in performance, which can greatly enhance the security of images during encryption and transmission.

Image encryption algorithm based on DNA mutation and a novel four-dimensional hyperchaos

Abstract Aiming at the problem that insufficient complexity of ordinary multi-dimensional chaotic systems and the cumbersome design of encryption algorithms without excellent encryption effects. This paper constructs a four-dimensional hyperchaotic system with high Lyapunov exponent and complex dynamic behavior. We designed an encryption algorithm based on point mutation, mutation diffusion, and folding mutation in DNA mutations. During the encryption process, we perform point mutation transformation on the entire base sequence, then spread the mutations one by one starting from the second base of the sequence, and finally flip every four base sequences according to folding mutations. The images encrypted by this algorithm have a uniform grayscale histogram, high information entropy, and high key sensitivity. It can resist exhaustive attacks, noise attacks, cropping attacks, and differential attacks, and have a fast encryption speed.

A hexadecimal scrambling image encryption scheme based on improved four-dimensional chaotic system

A hexadecimal scrambling image encryption scheme based on improved four-dimensional chaotic system

Reform of four-dimensional integration curriculum system of “on-the-job competition certificate” for new engineering electronic information majors

Since the beginning of 2021, the importance of the development of “Industrial Internet” and “Metauniverse” has been mentioned many times in many important documents such as the outline of the 14th Five-Year Plan and the 2021 government work report. Under the background that the industrial Internet has replaced the consumer Internet as the main direction, with the change of digital electronic information technology and the huge demand of the market, the new engineering electronic information specialty will face great opportunities and challenges. Education needs to cultivate a large number of differentiated talents and individualized skilled talents. Therefore, vocational education is the guarantee of social talents in the process of promoting modern industrialization. Therefore, it is necessary to focus on the major strategy set by the state, closely connect with industrial upgrading, grasp the trend of technological change, promote the integration of production and education, and thoroughly implement the vocational skill grade certificate system. Moreover, the comprehensive education mechanism of “post-class competition certificate” should be promoted. Under the above background, aiming at the demand of electronic information major in new engineering, this paper puts forward the curriculum system reform of “post-class competition certificate”, and analyzes the practice process. On this basis, it completes the integration of teaching content and post work cases, realizes the docking of teaching mode and post work process, and finally realizes the matching of course examination and professional grade certificate standard. Besides, it can also improve curriculum resources, improve the composition of teaching staff, create high-quality curriculum training conditions, etc., and finally promote the rapid development of electronic information industry.

On a solvable four-dimensional system of difference equations

Abstract In this paper we show that the following four-dimensional system of difference equations x n + 1 = y n α z n − 1 β , y n + 1 = z n γ t n − 1 δ , z n + 1 = t n ϵ x n − 1 μ , t n + 1 = x n ξ y n − 1 ρ , n ∈ N 0 , $$\begin{array}{} \displaystyle x_{n+1}=y_{n}^{\alpha}z_{n-1}^{\beta}, \quad y_{n+1}=z_{n}^{\gamma}t_{n-1}^{\delta}, \quad z_{n+1}=t_{n}^{\epsilon}x_{n-1}^{\mu}, \quad t_{n+1}=x_{n}^{\xi}y_{n-1}^{\rho}, \qquad n\in \mathbb{N}_{0}, \end{array}$$ where the parameters α, β, γ, δ, ϵ, μ, ξ, ρ ∈ ℤ and the initial values x –i , y –i , z –i , t –i , i ∈ {0, 1}, are real numbers, can be solved in closed forms, extending further some results in literature.

Global Mittag-Leffler Attractive Sets, Boundedness, and Finite-Time Stabilization in Novel Chaotic 4D Supply Chain Models with Fractional Order Form

This research explores the complex dynamics of a Novel Four-Dimensional Fractional Supply Chain System (NFDFSCS) that integrates a quadratic interaction term involving the actual demand of customers and the inventory level of distributors. The introduction of the quadratic term results in significantly larger maximal Lyapunov exponents (MLE) compared to the original model, indicating increased system complexity. The existence, uniqueness, and Ulam–Hyers stability of the proposed system are verified. Additionally, we establish the global Mittag-Leffler attractive set (MLAS) and Mittag-Leffler positive invariant set (MLPIS) for the system. Numerical simulations and MATLAB phase portraits demonstrate the chaotic nature of the proposed system. Furthermore, a dynamical analysis achieves verification via the Lyapunov exponents, a bifurcation diagram, a 0–1 test, and a complexity analysis. A new numerical approximation method is proposed to solve non-linear fractional differential equations, utilizing fractional differentiation with a non-singular and non-local kernel. These numerical simulations illustrate the primary findings, showing that both external and internal factors can accelerate the process. Furthermore, a robust control scheme is designed to stabilize the system in finite time, effectively suppressing chaotic behaviors. The theoretical findings are supported by the numerical results, highlighting the effectiveness of the control strategy and its potential application in real-world supply chain management (SCM).

Control of Hopf bifurcation for a four-dimensional fractional order hyperchaotic system with coexisting attractors

Control of Hopf bifurcation for a four-dimensional fractional order hyperchaotic system with coexisting attractors