Four-dimensional System Research Articles

An epidemic dynamics model with limited isolation capacity.

We consider a modified SIR model with a four-dimensional system of ordinary differential equations to consider the influence of a limited isolation capacity on the final epidemic size defined as the total number of individuals who experienced the disease at the end of an epidemic season. We derive the necessary and sufficient condition that the isolation reaches the capacity in a finite time on the way of the epidemic process, and show that the final epidemic size is monotonically decreasing in terms of the isolation capacity. We find further that the final epidemic size could have a discontinuous change at the critical value of isolation capacity below which the isolation reaches the capacity in a finite time. Our results imply that the breakdown of isolation with a limited capacity would cause a drastic increase of the epidemic size. Insufficient capacity of the isolation could lead to an unexpectedly severe epidemic situation, while such a severity would be avoidable with the sufficient isolation capacity.

A hierarchical intervention scheme based on epidemic severity in a community network.

As there are no targeted medicines or vaccines for newly emerging infectious diseases, isolation among communities (villages, cities, or countries) is one of the most effective intervention measures. As such, the number of intercommunity edges ([Formula: see text]) becomes one of the most important factor in isolating a place since it is closely related to normal life. Unfortunately, how [Formula: see text] affects epidemic spread is still poorly understood. In this paper, we quantitatively analyzed the impact of [Formula: see text] on infectious disease transmission by establishing a four-dimensional [Formula: see text] edge-based compartmental model with two communities. The basic reproduction number [Formula: see text] is explicitly obtained subject to [Formula: see text] [Formula: see text]. Furthermore, according to [Formula: see text] with zero [Formula: see text], epidemics spread could be classified into two cases. When [Formula: see text] for the case 2, epidemics occur with at least one of the reproduction numbers within communities greater than one, and otherwise when [Formula: see text] for case 1, both reproduction numbers within communities are less than one. Remarkably, in case 1, whether epidemics break out strongly depends on intercommunity edges. Then, the outbreak threshold in regard to [Formula: see text] is also explicitly obtained, below which epidemics vanish, and otherwise break out. The above two cases form a severity-based hierarchical intervention scheme for epidemics. It is then applied to the SARS outbreak in Singapore, verifying the validity of our scheme. In addition, the final size of the system is gained by demonstrating the existence of positive equilibrium in a four-dimensional coupled system. Theoretical results are also validated through numerical simulation in networks with the Poisson and Power law distributions, respectively. Our results provide a new insight into controlling epidemics.

A SULAPA EPPE’E MODEL CONSTRUCTION FOR THE LEGAL PROTECTION OF THE LIFE ENVIRONMENT IN THE COASTAL FISHING RESOURCE EXPLOITATION AT SOUTH SULAWESI PROVINCE

This research analyzes the construction model of Sulapa Eppe'e in environmental law protection for the utilization of coastal fishery resources. This type of research uses a normative-empirical constructivism paradigm. The results of the study show that Sulapa Eppe'e adheres to a four-dimensional system of legal relations that places humans as the center in relations with God, nature (environment), society, and the government and the state. Model construction includes: concepts, philosophies, paradigms, ideologies, basic values, norms, principles, analytical methods and practices. This model gave birth to three pillars of wisdom, namely local wisdom, ecological wisdom, and the legal wisdom of the Mampanre'tasi tradition (conservation and zoning system), Rompong (protection and management system), Pemali and Palili'(prevention and repressive system), Mamia Kadialo (ecological wisdom values), Ponggawa – sawi (coordination and cooperation system). The Sulapa Eppe'e model can play an important role in overcoming tensions, integrating and harmonizing political products, ecological products and cultural products from environmental law.

Constructions of b-semitoric systems

In this article, we introduce b-semitoric systems as a generalization of semitoric systems, specifically tailored for b-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the distinctive characteristics of these systems. A b-semitoric system is a four-dimensional b-integrable system that satisfies certain conditions: one of its momentum map components is proper and generates an effective global S1-action and all singular points are non-degenerate and devoid of hyperbolic components. To illustrate this concept, we provide five examples of b-semitoric systems by modifying the coupled spin oscillator and the coupled angular momenta, and we also classify their singular points. Additionally, we describe the dynamics of these systems through the image of their respective momentum maps.

Dynamics and Circuit Implementation of a 4D Memristive Chaotic System with Extreme Multistability

In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with cosine function is constructed. It has infinitely many equilibria. By changing the initial values [Formula: see text], [Formula: see text] and [Formula: see text] of the system and keeping the parameters constant, we obtained the distribution of infinitely many single-wing and double-wing attractors along the [Formula: see text]-coordinate, which verifies the initial-offset boosting behavior of the system. Then the complex dynamical behavior of the system is studied in detail through the phase portraits of coexisting attractors, the average value of state variables, Lyapunov exponent spectrum, bifurcation diagram, attraction basin and the complexity of spectral entropy (SE). In addition, the simulation of the Multisim circuit is also carried out, and the results of numerical simulation and analog circuit simulation are consistent. Finally, the chaotic sequence generated by the system is applied to image encryption, and according to the performance analysis, the proposed chaotic system has good security performance.

Multistability in a Circulant Dynamical System

In this paper we report on a two parameter four-dimensional dynamical system with cyclic symmetry, namely a circulant dynamical system. This system is a twelve-term polynomial system with four cubic nonlinearities. Reported are some parameter-space diagrams for this system, all of them considering the same range of parameters, but generated from different initial conditions. We show that such diagrams display the occurrence of multistability in this system. Properly generated bifurcation diagrams confirm this finding. Basins of attraction of coexisting attractors in the related phase-space are presented, as well as an example showing phase portraits for periodic and chaotic coexisting attractors.

Economic system forecasting based on temporal fusion transformers: Multi-dimensional evaluation and cross-model comparative analysis

Although helpful in reducing the uncertainty associated with economic activities, economic forecasting often suffers from low accuracy. Recognizing the high compatibility between deep learning and the nonlinear characteristics of socioeconomic systems, in this paper, we introduce state-of-the-art temporal fusion transformers (TFTs) into the field of economic system forecasting and predict the performance of the Chinese macroeconomic system. Based on an extended analysis of gross final product (GFP) and the intertemporal dynamic relationship between demand-side indicators and output indicators, we establish a scientific economic forecasting framework. To summarize the forecasting characteristics of the TFT algorithm, we compare its one-step and three-step modeling effects in forecasting output indicators with a series of representative benchmark models. According to our proposed four-dimensional evaluation system, the forecasts for China’s macroeconomic system provided by the TFT model have obvious advantages in terms of overall stability, forecasting efficiency, reduction of numerical and timing errors, direction accuracy, and turning point accuracy. The forecast results show that China’s economy faces a risk of slowing growth in the post-pandemic period.

Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

In this paper, the fractional-order chaotic system form of a four-dimensional system with cross-product nonlinearities is introduced. The stability of the equilibrium points of the system and then the feedback control design to achieve this goal have been analyzed. Furthermore, further dynamical behaviors including, phase portraits, bifurcation diagrams, and the largest Lyapunov exponent are presented. Finally, the global Mittag–Leffler attractive sets (MLASs) and Mittag–Leffler positive invariant sets (MLPISs) of the considered fractional order system are presented. Numerical simulations are provided to show the effectiveness of the results.

Image encryption algorithm using multi-base diffusion and a new four-dimensional chaotic system

Image encryption algorithm using multi-base diffusion and a new four-dimensional chaotic system

Dynamical analysis of a novel chaotic system and its application to image encryption

This study presents a novel four-dimensional chaotic system derived from the Lorenz-Haken equation. The paper investigates the system’s dissipative properties, equilibrium point, Poincaré map, 0–1 test, Lyapunov exponent, complexity, and bifurcation diagram to introduce the system’s dynamics. The research also examines the chaotic behavior of the system under various parameters, demonstrating the existence of symmetric attractors and offset boosting. To demonstrate the system’s feasibility, circuit simulation is performed using Multisim software, and the hardware implementation is carried out using a Field Programmable Gate Array (FPGA). An image encryption algorithm is designed by integrating matrix dislocation, backward diffusion, and deoxyribonucleic acid (DNA) encryption with the discretized chaotic system. The simulation results show that the algorithm has a good encryption effect. NIST tests show that the sequence has good randomness, correlation coefficient, and information entropy tests show that the encrypted image has strong randomness, and key space and key sensitivity prove that the system has a good ability to resist exhaustive attacks. The use of simulated differential attacks, cropping attacks, and noise attacks has demonstrated the high robustness of the system. The use of peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index proves that the encryption algorithm does not affect image quality. Further proving the excellent performance of the proposed encryption algorithm.

Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System

In this paper, a new four-dimensional (4D) hyperchaotic biplane system is designed and presented. The dynamical properties of this new system are studied by means of tools such as bifurcation diagrams, Lyapunov exponents and phase diagrams. The Hopf bifurcation and periodic solutions of this hyperchaotic system are solved analytically. In addition, a new hyperchaotic control strategy is applied, and a comparative analysis of the controlled system is performed.

Modeling and complexity analysis of a fractional-order memristor conservative chaotic system

Memristors are often utilized in circuit model analysis as one of the fundamental circuit components. In this paper, a five-dimensional conservative memristor chaotic system is built after the introduction of the memristor into a four-dimensional conservative chaotic system. The dynamic changes of the system are examined using phase diagram, mean value, and Lyapunov exponent spectrum. A line equilibrium point, symmetry and multi-stability are characteristics of the system; the phase trajectory can also produce shrinking and structure transformation behavior with the change of parameters. Furthermore, the system has initial offset boosting behaviors, conservative flows of it can be altered in position by changing two initial values, respectively. Most notably, we discover that the complexity of the system rises with the inclusion of memristor and again with the addition of fractional differential operators. It is shown that the complexity of chaotic systems may increase with the addition of memristors and fractional-order differential operators. At last, the NIST is used to test the randomness of the sequence, and the system's physical realizability is confirmed by the DSP platform.

Rucklidge-based memristive chaotic system: Dynamic analysis and image encryption

A new four-dimensional (4D) memristive chaotic system is obtained by introducing a memristor into the Rucklidge chaotic system, and a detailed dynamic analysis of the system is performed. The sensitivity of the system to parameters allows it obtains 16 different attractors by changing only one parameter. The various transient behaviors and excellent spectral entropy and C0 complexity values of the system can also reflect the high complexity of the system. A circuit is designed and verified the feasibility of the system from the physical level. Finally, the system is applied to image encryption, and the security of the encryption system is analyzed from multiple aspects, providing a reference for the application of such memristive chaotic systems.

Four-dimensional dose reconstruction system for lung cancer VMAT treatment: a 4D phantom study

Four-dimensional dose reconstruction system for lung cancer VMAT treatment: a 4D phantom study

Efficient image encryption algorithm based on dynamic high-performance S-box and hyperchaotic system

With the development of information technology, security, low latency, and instant messaging have become a major demand. To solve this problem, this paper designs a secure and efficient image cipher algorithm. Firstly, a new four-dimensional hyperchaotic system with strong chaotic performance is proposed. Secondly, a dynamic high-performance S-box generation algorithm is proposed based on GF(28) by improving the method of generating S-boxes in AES, selecting suitable irreducible polynomial as well as affine matrix, precomputing the corresponding affine multiplication matrix as well as multiplication inverse matrix. The S-box algebraic expressions generated by this algorithm have 255 terms and are more resistant to algebraic attacks than AES. Finally, based on the four-dimensional hyperchaotic system and dynamic high-performance S-box generation algorithm, the new image cipher algorithm that can encrypt and decrypt images of arbitrary size is proposed. The image cipher algorithm consists of two rounds of interleaved permutation, two rounds of dynamic S-box substitution and cyclic shift permutation with fixed point. Cyclic shift permutation with fixed point and dynamic S-box substitution ensure that the plaintext transformation can be transferred to the entire image. Through testing, analysis and comparison, the algorithm has proven to be a secure and efficient image cipher algorithm.

Fractional mode charge of higher-order topological acoustic transport

The local density of states (LDOS), which describes the space-resolved density of states, has been studied in the context of exploring topological materials. Here, we report the observation of the fractional mode charge of topological states in a four-dimensional synthetic acoustic system, which is based on coupled acoustic cavities. We experimentally measured the LDOS of topological boundary states and corner states of this system and observed one-half and one-quarter fractional mode charges. In addition, we also obtained the LDOS in a three-dimensional acoustic system by simulation and observed the one-eighth fractional mode charge of the system. The results show that the appearance of topological states can correspond to the fractional charges, which is useful for the understanding of topology in acoustic systems and provides a new method for the characterization of topological states in topological acoustic systems.

Higher-order topological sound transport in synthetic spaces

We design a four-dimensional system with straight waveguides composed of coordinate-dependent coupled waveguides. By controlling the phase in synthetic space and the excitation of the corresponding sound source mode, we show that the pumping incorporating adiabatic modulation of discretely varied coupling waveguides along a given orbit in the phason space occurs only in specific space directions. In addition, robust corner-to-corner topological pumping is achieved in finite-sized two-dimensional modulated acoustic structures. Our results provide a general strategy to achieve topological pumping through discrete property modulations and pave new paths for studying higher-dimensional topological phases in discrete systems.

A new four-dimensional hyper-chaotic system for image encryption

<span lang="EN-US">Currently, images are very important with the rapid growth of communication networks. Therefore, image encryption is a process to provide security for private information and prevent unwanted access to sensitive data by unauthorized individuals. Chaos systems provide an important role for key generation, with high randomization properties and accurate performance. In this study, a new four-dimensional hyper-chaotic system has been suggested that is used in the keys generation, which are utilized in the image encryption process to achieve permutation and substitution operations. Firstly, color bands are permuted using the index of the chaotic sequences to remove the high correlation among neighboring pixels. Secondly, dynamic S-boxes achieve the principle of substitution, which are utilized to diffuse the pixel values of the color image. The efficiency of the proposed method is tested by the key space, histogram, and so on. Security analysis shows that the proposed method for encrypting images is secure and resistant to different attacks. It contains a big key space of (2627) and a high sensitivity to a slight change in the secret key, a fairly uniform histogram, and entropy values nearby to the best value of 8. Moreover, it consumes a very short time for encryption and decryption.</span>

Finite-time Synchronization of the 4-D Hyper-chaotic Chen-Qi-like System

For Chen-Qi-like four-dimensional hyper-chaotic system, controllers designed with Lyapunov stability theory to achieve synchronous/anti- synchronous control of chaos are found that sometimes synchronization errors do not decrease to zero in finite time. To solve it, a new controller and parameter estimation law are proposed to achieve finite-time synchronization. The stability analysis of the closed-loop dynamics is derived and the effectiveness of the theoretical results is testified. Taking the parameters L=2, μ=0.5, the state time history diagram and the synchronous error curve are investigated via numerical simulation, which show that the synchronization errors are zero in finite time while two systems in chaotic motion, but synchronization error of the state with cubic nonlinearity is not zero in finite time while two systems in periodic motion; Adjust L=200,μ=0.5, numerical simulation again, then all the errors are zero in finite time. Thus the effectiveness is verified.

Novel chaos based cryptosystem using four-dimensional hyper chaotic map with efficient permutation and substitution techniques

In this paper, a competent hyper chaos-based image encryption technique is proposed. The cryptosystem uses a four-dimensional hyper chaotic map for implementing the secret key information. In terms of Lyapunov exponents, NIST test results and bifurcation diagrams, 4-D hyperchaotic system exhibits better dynamical behavior than lower dimensional chaotic systems. Also, 4-D map has superior hyperchaotic performance in views of ergodicity, complexity, and randomness behavior and is capable to generate an unpredictable keystream, which is highly suitable for encryption. Therefore, a novel image encryption algorithm using four-dimensional hyper chaotic system is proposed here. A novel method with sequence of mathematical operations is used for the secret key generation. Both the confusion and diffusion phases are implemented on the basis of this secrete random values with innovative designs. In permutation phase, keystream-based pixel level and bit level scrambling are performed to shuffle the image pixels effectively. Novel methods are implemented to accomplish pixel level scrambling with row and column shift operations. The bit level scrambling is also instigated with a novel cyclic rotation technique. Thus, the pixel level and bit level scrambling ensure higher security in the permutation process. In substitution phase, the keystream is XORed with scrambled images in an effective manner to obtain the final encrypted image. Various evaluation measures are used to access the safety and security of the proposed system. The evaluation result of the projected method with numerous other techniques shows the sovereignty and higher security of the planned technique. The keystreams are generated from the hyperchaotic Lorenz system using a novel approach, and its generation is completely independent of the original image. The algorithm has wider application prospects, including encryption of images in medical field and cloud environment.