Analysis of transition between chaos and hyper-chaos of an improved hyper-chaotic system

An improved hyper-chaotic system based on the hyper-chaos generated from Chen＇s system is presented, and some basic dynamical properties of the system are investigated by means of Lyapunov exponent spectrum, bifurcation diagrams and characteristic equation roots. Simulations show that the new improved system evolves into hyper-chaotic, chaotic, various quasi-periodic or periodic orbits when one parameter of the system is fixed to be a certain value while the other one is variable. Some computer simulations and bifurcation analyses are given to testify the findings.

Analytical criteria for local activity of CNN with five state variables and application to Hyper-chaos synchronization Chua's circuit

The analytic criteria for the local activity theory in one-port cellularneural network (CNN) with five local state variables are presented. The application to a Hyper-chaossynchronization Chua's circuit (HCSCC) CNN with 1125 variables is studied. The bifurcation diagramsof the HCSCC CNN show that they are slightly different from the smoothed CNN with one or two portsand four state variables calculated earlier. The evolution of the patterns of the state variables ofthe HCSCC CNN is stimulated. Oscillatory patterns, chaotic patterns, convergent or divergentpatterns may emerge if the selected cell parameters are located in the locally active domains butnearby or in the edge of chaos domain.

Five-dimensional teleparallel theory equivalent to general relativity,the axially symmetric solution,energy and spatial momentum

A theory of （4＋1）-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields （pentad）, defined globally on a manifold M, and gravity is attributed to the torsion. The Lagrangian density is quadratic in the torsion tensor. We then give the exact five-dimensional solution. The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity. We also use the definition of the gravitational energy to calculate the energy and the spatial momentum.

Hyper-chaos encryption using convolutional masking and model free unmasking

In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative.

Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.

Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system

In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic attractor in wide parameters regions. By using the center manifold theorem and the local bifurcation theory, a pitchfork bifurcation is demonstrated to arise at the zero equilibrium point. Numerical analysis demonstrates that the hyper-cha^tic system can generate complex dynamical behaviors, e.g., a direct transition from quasi-periodic behavior to hyper-chaotic behavior. Finally, an electronic circuit is designed to implement the hyper-chaotic system, the experimental results are consist with the numerical simulations, which verifies the existence of the hyper-chaotic attractor. Due to the complex dynamic behaviors, this new hyper-cha^tic system is useful in the secure communication.

One-way hash function based on hyper-chaotic cellular neural network

The design of an efficient one-way hash function with good performance is a hot spot in modern cryptography researches. In this paper, a hash function construction method based on cell neural network with hyper-chaos characteristics is proposed. First, the chaos sequence is gotten by iterating cellular neural network with Runge Kutta algorithm, and then the chaos sequence is iterated with the message. The hash code is obtained through the corre- sponding transform of the latter chaos sequence. Simulation and analysis demonstrate that the new method has the merit of convenience, high sensitivity to initial values, good hash performance, especially the strong stability.

5DGWO-GAN:A Novel Five-Dimensional Gray Wolf Optimizer for Generative Adversarial Network-Enabled Intrusion Detection in IoT Systems

The Internet of Things(IoT)is integral to modern infrastructure,enabling connectivity among a wide range of devices from home automation to industrial control systems.With the exponential increase in data generated by these interconnected devices,robust anomaly detection mechanisms are essential.Anomaly detection in this dynamic environment necessitates methods that can accurately distinguish between normal and anomalous behavior by learning intricate patterns.This paper presents a novel approach utilizing generative adversarial networks(GANs)for anomaly detection in IoT systems.However,optimizing GANs involves tuning hyper-parameters such as learning rate,batch size,and optimization algorithms,which can be challenging due to the non-convex nature of GAN loss functions.To address this,we propose a five-dimensional Gray wolf optimizer(5DGWO)to optimize GAN hyper-parameters.The 5DGWO introduces two new types of wolves:gamma(γ)for improved exploitation and convergence,and theta(θ)for enhanced exploration and escaping local minima.The proposed system framework comprises four key stages:1)preprocessing,2)generative model training,3)autoencoder(AE)training,and 4)predictive model training.The generative models are utilized to assist the AE training,and the final predictive models(including convolutional neural network(CNN),deep belief network(DBN),recurrent neural network(RNN),random forest(RF),and extreme gradient boosting(XGBoost))are trained using the generated data and AE-encoded features.We evaluated the system on three benchmark datasets:NSL-KDD,UNSW-NB15,and IoT-23.Experiments conducted on diverse IoT datasets show that our method outperforms existing anomaly detection strategies and significantly reduces false positives.The 5DGWO-GAN-CNNAE exhibits superior performance in various metrics,including accuracy,recall,precision,root mean square error(RMSE),and convergence trend.The proposed 5DGWO-GAN-CNNAE achieved the lowest RMSE values across the NSL-KDD,UNSW-NB15,and IoT-23 datasets,with values of 0.24,1.10,and 0.09,respectively.Additionally,it attained the highest accuracy,ranging from 94%to 100%.These results suggest a promising direction for future IoT security frameworks,offering a scalable and efficient solution to safeguard against evolving cyber threats.

Moments of inertia of triaxial nuclei in covariant density functional theory

The covariant density functional theory(CDFT)and five-dimensional collective Hamiltonian(5DCH)are used to analyze the experimental deformation parameters and moments of inertia(MoIs)of 12 triaxial nuclei as extracted by Allmond and Wood[J.M.Allmond and J.L.Wood,Phys.Lett.B 767,226(2017)].We find that the CDFT MoIs are generally smaller than the experimental values but exhibit qualitative consistency with the irrotational flow and experimental data for the relative MoIs,indicating that the intermediate axis exhibites the largest MoI.Additionally,it is found that the pairing interaction collapse could result in nuclei behaving as a rigid-body flow,as exhibited in the^(186-192)Os case.Furthermore,by incorporating enhanced CDFT MoIs(factor of f≈1.55)into the 5DCH,the experimental low-lying energy spectra and deformation parameters are reproduced successfully.Compared with both CDFT and the triaxial rotor model,the 5DCH demonstrates superior agreement with the experimental deformation parameters and low-lying energy spectra,respectively,emphasizing the importance of considering shape fluctuations.

Sr,Nd and Pb isotopic characteristics of granulite and pyroxenite xenoliths from Hannuoba Basalts in five-dimensional space and their geological implications

Sr, Nd and Pb isotopic characteristics of granulite and pyroxenite xenoliths from Hannuoba Basalts in five-dimensional space are studied. Combined with the distribution of xenoliths, it is suggested that the isotopic relationship between various xenoliths can be well explained by the processes of delamination.

Experimental and numerical study of water sprayed turbulent combustion: Proposal of a neural network modeling for five-dimensional flamelet approach

Owing to the increasing worldwide demand for natural gas,the development of a large submerged combustion vaporizer is required.Its burner is equipped with a water spray nozzle to reduce nitrogen oxides,and a practi-cal simulation method is required for the optimal design.The non-adiabatic flamelet approach can predict the combustion emissions and is useful for reducing simulation costs.However,as the number of control variables increases,the database requires larger memory and cannot be dealt with by general computers.In this study,an artificial neural network(ANN)model based on a five-dimensional flamelet database,which includes the effects of heat loss and vapor concentration by sprayed water evaporation,is developed.Furthermore,large eddy sim-ulations(LESs)for turbulent combustion fields with and without water spray are conducted employing flamelet generated manifold(FGM)approach with this ANN model,and the validity is investigated.For comparison,a lab-scale burner equipped with a water spray nozzle is manufactured,and combustion experiments with and without water spray are conducted.The results show that CO,NO,temperature,and reaction rate of progress variable predicted by the present ANN model are in good agreement with those of a five-dimensional flamelet database.In the condition without water spray,the flame behavior predicted by the LES employing the FGM/ANN ap-proach is in good agreement with that employing the conventional FGM approach,while indicating much lower memory,although there appeared some quantitative discrepancies in the temperature against the experiment probably partially because of the insufficiency of the FGM approach for the present complex flame structure.In the condition with water spray,the LES employing the FGM/ANN approach is able to capture the effect of the water spray on the flame behavior in the experiment,such that the water spray decreases the temperature,which causes the decrease in NO but increase in CO.

Can Thermal Input from a Prior Universe Account for Relic Graviton Production and Imply Usage of the Bogomolnyi Inequality, as a Bridge between Brane World Models and Loop Quantum Gravity in Early Universe Conditions?

The author uses a low temperature and low entropy pre inflation state to create a bridge between String theory and loop quantum gravity. We use this analysis in lieu of the CMB barrier as of z = 1000 since it is our way to come up with a working model of quintessence scalar fields, which permits relic generation of dark matter and dark energy. Not only referencing this bridge, we do it in such a way as to utilize the low entropy condition which the Brane world model of Randal and Sundrum creates, and to show how it is in common with what Caroll and Chen wrote up in 2005., i.e. when the universe was about 1000 times smaller and 100,000 times younger than today.

Does a Randall-Sundrum Brane World Effective Potential Influence Axion Walls Helping to Form a Cosmological Constant Affecting Inflation?

In 2003, Guth posed the following question in a KITP seminar in UCSB. Namely “Even if there exist 101000 vacuum states produced by String theory, does inflation produce overwhelmingly one preferred type of vacuum states over the other possible types of vacuum states”? This document tries to answer how a preferred vacuum state could be produced, and by what sort of process. We construct a di quark condensate leading to a cosmological constant in line with known physical observations. We use a phase transition bridge from a tilted washboard potential to the chaotic inflationary model pioneered by Guth which is congruent with the slow roll criteria. This permits criteria for initiation of graviton production from a domain wall formed after a transition to a chaotic inflationary potential. It also permits investigation of if or not axion wall contributions to inflation are necessary. If we reject an explicit axion mass drop off to infinitesimal values at high temperatures, we may use the Bogomolnyi inequality to rescale and reset initial conditions for the chaotic inflationary potential. Then the Randall-Sundrum brane world effective potential delineates the end of the dominant role of di quarks, and the beginning of inflation. And perhaps answers Freeman Dysons contention that Graviton production is unlikely given present astrophysical constraints upon detector systems. We end this with a description in the last appendix entry, Appendix VI, as to why, given the emphasis upon di quarks, as to the usefulness of using times before Planck time interval as to modeling our physical system and its importance as to emergent field structures used for cosmological modeling.

Transition From Hyper－Chaotic State to Quasi－Steady State in a Spailally Distributed Nonlinear System

The dynamic characteristic in a spatially distributed nonlinear system, a subset of lasers in an array of coupled lasers, has been studied and analysed numerically. The evolution, with the increasing coupling strength,from stable quiescent state to chaotic state, to hyper-chaotic state and, back to quasi-steady state has been observed in this system.

Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity

A theory of（N＋1）-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity（TEGR）.The fundamental gravitational field variables are the（N＋1）-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution（Schwarzschild（4＋1）-dimensions）.Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.

Dynamic evaluation of traffic flows on city roads

This paper presents an analysis of the random fluctuations, deferred conduction effect and periodicity of road traffic based on the basic features of road networks. It also discusses the limitations of road network evaluation theories based on road "V/C". In addition, it proposes a set of theoretical and technical methods for the real-time evaluation of traffic flows for entire road networks, and for solving key technical issues, such as real-time data collection and processing in areas with no blind zones, the spatial-temporal dynamic analysis of road network traffic, and the calibration of key performance index thresholds. It also provides new technical tools for the strategic transportation planning and real-time diagnosis of road traffic. The new tools and methodology presented in this paper are validated using a case study in Beijing.

5D Hyper-Chaotic System with Multiple Types of Equilibrium Points

A chaotic system with various equilibrium types has rich dynamic behaviors.Its state can switch flexibly among different families of attractors,which is beneficial to the practical applications.So it has been widely concerned in recent years.In this paper,a new 5D hyper-chaotic system is proposed.The important characteristic of the system is that it may have multiple types of equilibrium points by changing system parameters,namely,linear equilibrium point,no equilibrium point,non-hyperbolic unstable equilibrium point and stable hyperbolictype equilibrium point.Furthermore,there are hyper-chaotic phenomena and multi-stability about the coexistence of multiple chaotic attractors and the coexistence of hyper-chaotic attractors and chaotic attractors in the system.In addition,the system,complexity is analyzed.It is found that the complexity is close to 1 in the hyper-chaotic state and a pseudo-random sequence generated by the system passes all the statistical tests.Finally,an analog circuit of the system is designed and simulated.

Architecture,application,and prospect of digital twin for highway infrastructure

The years we are experiencing are often identified as those of the age of digital technologies,where“digital”is commonly associated with intelligence,efficiency,and convenience.The emergence of digital technologies has significantly impacted and transformed various aspects of our society compared to the past.In this panorama,some arising questions regard transportation infrastructure systems and,first of all,highway infrastructure.This research focuses on one central issue:how highways fit into this digital revolution.Actually,the work in this paper can be described as follows.Although there are many different theoretical model systems for the architecture of the digital twin,we have chosen to review the main body of research on the digital twin in highway infrastructure based on a relatively well-established modeling framework,the five-dimensional model of the digital twin.After discussing the components of the digital twin for highway infrastructure's five-dimensional model,the paper reviews some innovative technologies that make these items effective.In addition to this,the digital twin maturity level of highway infrastructure and the MBSE-based(model-based systems engineering)digital twin model for highway are also discussed in this paper.Therefore,the paper provides a bird's eye view of this extremely dynamic technology for a new system of intelligent highways and discusses some of their criticalities and strengths,allowing for the optimization and development of new transportation functions and services,improving the adaptability of highways to the digital revolution.

Microscopic analysis of spherical to γ-soft shape transitions in Zn isotopes

The rapid transition between spherical and γ-soft shapes in Zn isotopes in the mass A 70 region,is analyzed using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom,with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes.The microscopic potential energy surfaces,together with the characteristic collective observables,illustrate a rapid transition from near spherical shape at the N = 40 subshell,to γ-soft deformed shapes for lighter isotopes.The calculated spectra display fingerprints of a second-order shape phase transition that can be approximately described by the E(5) analytic solution.