Chaotic Model Research Articles

Real time hybrid medical image encryption algorithm combining memristor-based chaos with DNA coding

Image encryption is a commonly used method to secure medical data on a public network, playing a crucial role in the healthcare industry. Because of their complex dynamics, memristors are often used in developing novel chaotic systems that can improve the efficiency of encryption algorithms based on chaos. In this work, we propose a novel locally active memristor-based chaotic circuit model and present a real time hybrid image encryption application developed on a PYNQ-Z1 (Python Productivity for Zynq) low-cost FPGA board using Jupiter programming environment. The proposed hybrid algorithm combines memristor-based chaos with a DNA (deoxyribonucleic acid) encryption algorithm exploiting diffusion-confusion technique. We initially present a new compact and inductorless chaotic circuit, derive the model equations, and then verify its chaotic dynamics numerically through the investigation of the phase portraits, Lyapunov exponents and the bifurcation diagrams. We further implement the chaotic circuit experimentally with discrete elements. The randomness of the chaotic sequence is improved using Trivium and von Neumann post-processor algorithms and assessed through the NIST tests. Finally, the performance of the encryption algorithm is evaluated through various metrics, including histogram and correlation analyses, differential attack, information entropy, as well as data-loss and noise attack, demonstrating its security and suitability for real-time encryption systems.

A non-degenerate n-dimensional integer domain chaotic map model with application to PRNG

To address the limitations of existing chaotic maps, we proposed a non-degenerate n-dimensional (n ≥ 2) integer domain chaotic map (nD-IDCM) model that can construct any non-degenerate n-dimensional integer domain chaotic maps. Moreover, we analyzed its chaotic behavior through Lyapunov exponent, and found that the nD-IDCM generates chaotic sequences in the integer domain, which effectively resolves the issue of finite precision effect when implementing existing chaotic maps on computers or digital devices. To verify the effectiveness of nD-IDCM, we presented two instances to demonstrate how the positive Lyapunov exponents can be regulated by manipulating the parameter matrix. Subsequently, we have scrutinized their dynamical behavior using Kolmogorov entropy, sample entropy, correlation dimension and randomness testing via TestU01. Finally, to assess the feasibility of nD-IDCM, we devised a keyed pseudo random number generator (PRNG) based on a 3D-IDCM that can ensure superior randomness and unpredictability. Experimental results indicated that integer domain chaotic maps constructed using nD-IDCM have desirable Lyapunov exponents and exhibit ergodicity within a sufficient larger chaotic range.

A numerical study on fractional order financial system with chaotic and Lyapunov stability analysis

In the last few decades, academic research has focused more on financial problems and poverty levels. These are among the two major challenges of the modern world today. To understand the challenge of financial crisis and poverty in societies. This paper explains a deterministic financial system of non linear differential equations. Which aim to provide recommendations to address the twin challenges. In this fractional chaotic model, memory and chaos are portrayed as effects on a system. Financial systems of fractional order have three compartments: interest rate x(t), investment demand rate y(t) and price indexes rate z(t). For the first time, the Legendre wavelet approximation is applied to fractional order financial systems. A major objective of this process is to convert fractional differential equations (FDEs) into algebraic equations by using Legendre wavelets and their fractional integral operators. For residual analysis, convergence and stability analysis, we have used iteration methods and Legendre wavelets. This study indicates good results between the approximate and numerical solutions and that this method is efficient and accurate. Using the iteration method, we prove that the solution exists, while the contraction theory proves its uniqueness. The findings of this study will be extremely useful for future financial management. We have demonstrated the applicability and effectiveness of these methods by analysing numerical simulations for the fractional order financial model and the numerical simulation has been calculated by MATLAB programming.

A two-phase spatiotemporal chaos-based protocol for data integrity in IoT

One of the biggest problems with Internet of Things (IoT) applications in the real world is ensuring data integrity. This problem becomes increasingly significant as IoT expands quickly across a variety of industries. This study presents a brand-new data integrity methodology for Internet of Things applications. The “sequence sharing” and “data exchange” stages of the suggested protocol are divided into two parts. During the first phase, each pair of nodes uses a new chaotic model for securely exchanging their identity information to generate a common sequence. This phase’s objectives include user authentication and timing calculations for the second phase of the recommended method’s packet validation phase. The recommended approach was tested in numerous settings, and various analyses were taken into account to guarantee its effectiveness. Also, the results were compared with the conventional data integrity control protocol of IoT. According to the results, the proposed method is an efficient and cost-effective integrity-ensuring mechanism with eliminates the need for third-party auditors and leads to reducing energy consumption and packet overhead. The results also show that the suggested approach is safe against a variety of threats and may be used as a successful integrity control mechanism in practical applications.

Optimization of chaotic light output in semiconductor laser systems based on multi-objective optimization algorithm.

Aiming at the weak performance of chaotic light output in semiconductor laser systems, the study designed a power control algorithm for semiconductor laser drive systems based on linear self-disturbance rejection control. Then the optimization parameters and scope were determined, and multi-objective optimization and direction preference algorithms were introduced. A chaotic optical performance optimization model based on improved multi-objective genetic algorithm was constructed using adaptive functions as evaluation indicators. These results confirmed that the larger the bandwidth of the controller, the faster the response speed of the resonant converter, but the stability was poor. When the input voltage underwent a sudden change, the current ripple coefficient of the PID algorithm was 0.55%. The linear active disturbance rejection control algorithm could ensure that the voltage and current maintained at the set values, and the output current of the algorithm was more stable when the load underwent sudden changes. The directional preference algorithm could further provide more valuable solutions on the basis of adaptive genetic algorithms. When the peak value of the autocorrelation function was equal to 0.2, the delay characteristics of chaotic light were effectively suppressed, having strong signal bandwidth and complexity. In summary, the constructed model has good application effects in optimizing chaotic optical performance and has certain positive significance for communication security.

A Study of An Image Encryption Model Based on Tent-Ushiki Chaotic Fusion

Aiming at the shortcomings of current image encryption, such as simple structure, few parameters and small key space, we propose the Tent-Ushiki chaotic mapping image encryption method based on the improved firefly optimization algorithm. First, a chaotic mapping model based on the fusion of Tent and Ushiki is proposed. Second, for the lack of parameter optimization in chaotic models in general, we introduce the firefly optimization algorithm and optimize the algorithm for the shortcomings in terms of the adaptive step size, the adjustment factor and the inertia weights. Finally, the improved firefly algorithm is used for the fusion of the chaotic parameters of Tent and Ushiki. In the simulation experiments, this paper’s algorithm performs well in the statistical analysis and adjacent element correlation of the classical image test and significantly outperforms the comparative algorithms in terms of information entropy and anti-attack, which demonstrates that the algorithm is able to optimize the image encryption effect better.

Constructing a non-degeneracy nD chaotic map model and counteracting dynamic degradation through adaptive impulsive perturbation

The characteristics of state point trajectory in phase space of a chaotic map, such as ergodicity, aperiodicity, broadband and noise-like, have been proved to be suitable for cryptography. However, some weaknesses, such as small key space, multiple bifurcations and dense windows that exist in some classic 1D and 2D chaotic maps, effect their practical application. To solve these problems, we constructed a non-degeneracy nD chaotic model, and instantiated it to obtain a 3D chaotic map (3D-NDCM), the dynamics analysis results demonstrated that the 3D-NDCM has a sufficiently large chaotic range, its state point trajectories has ergodicity in phase space. To counteract dynamic degradation and extend the aperiodic length of state time sequences, we further constructed a 6D-NDCM based on the model. Experimental analysis results demonstrated that, a state time sequence with longer aperiodicity can be obtained, through both dimension expansion and adaptive impulsive perturbation.

Dynamics of chaotic and hyperchaotic modified nonlinear Schrödinger equations and their compound synchronization

We present in this paper four versions of chaotic and hyperchaotic modified nonlinear Schrödinger equations (MNSEs). These versions are hyperchaotic integer order, hyperchaotic commensurate fractional order, chaotic non-commensurate fractional order, and chaotic distributed order MNSEs. These models are regarded as extensions of previous models found in literature. We also studied their dynamics which include symmetry, stability, chaotic and hyperchaotic solutions. The sufficient condition is stated as a theorem to study the existence and uniqueness of the solutions of hyperchaotic integer order MNSE. We state and prove another theorem to test the dependence of the solution of hyperchaotic integer order MNSE on initial conditions. By similar way, we can introduce the previous two theorems for the other versions of MNSEs. The Runge-Kutta of the order 4, the Predictor-Corrector and the modified spectral numerical methods are used to evaluate the numerical solutions for integer, fractional and distributed orders MNSEs, respectively. We calculate numerically using the Lyapunov exponents the intervals of parameters of the purposed models at which hyperchaotic, chaotic and stable solutions are exist. The MNSEs have an important role in many fields of science and technology, such as nonlinear optics, electromagnetic theory, superconductivity, chemical and biological dynamics, lasers and plasmas. The compound synchronization for these chaotic and hyperchaotic models is investigated. We state its scheme using the tracking control technique among three integer commensurate and non-commensurate orders as the derive models and one distributed order as a slave model. We presented and proved a theorem that provides us with the analytical formula for the control functions which are required to achieve compound synchronization. The analytical results are supported by numerical calculations and agreement is found.

A new chaotic system and its practical applications in substitution box and random number generator

AbstractOne of the successful practical applications of chaos theory and nonlinear dynamics is chaos-based cryptology studies. In this study, a new chaotic system is proposed. The proposed chaotic system generator model has a simple algorithmic structure. In addition to, generated chaotic systems have rich dynamics. It has been examined whether this system has potential advantages, especially for information security applications. As a result of the analysis and experimental studies, it is seen that the study makes many contributions to the literature. The simple mathematical generator structure has the potential to reduce computational complexity, which is an important problem for cryptology applications. One of the most comprehensive studies has been realized for chaos-based substitution box designs. 70,000 different substitution box structures have been generated. It has been known that the highest nonlinearity value that can be achieved for designs that transform chaotic system outputs into substitution box structures is 106.75 today. It has been shown that this value may be higher. The new highest nonlinearity value is calculated as 107. Side channel analysis has been examined for substitution box structures with the highest nonlinearity value among the substitution boxes generated in the study. Analysis results show that the proposed new substitution box structures may have an advantage for application-oriented attacks. Among the generated substitution box structures, 289 substitution box structures with a nonlinearity value of 106 and above are presented as a public dataset for researchers to use. In addition, 3 different random sequences with a length of 1 million-bit were produced with the proposed map, and the NIST SP 800–22 test was applied. Test results for all datasets were successful. In this way, the proposed map can also be used as a random number generator.

A novel secure communication system using Duffing's chaotic model

A novel secure communication system using Duffing's chaotic model

Using a Chaotic Digital System to Generate Random Numbers for Secure Communication on 5G Networks

There are several encryption system applications in 5G networks where rapid response is needed, particularly in the military, health sector, traffic, and vehicular movement. This article presents a proposed data security system for 5G networks that fortifies the security of the network through the use of synchronized chaotic systems to produce pseudo-random numbers. The technique by which random numbers are generated during the encryption procedures is closely associated with 5G network security. Many synchronized chaotic systems are used to produce chaotic random models which are used as encryption bases for a wide variety of data. In this study, the encryption was carried out using a variety of data, including two and three-dimensional color images and audio signals of varying lengths, in addition to the use of Fast Fourier Transform (FFT) for encryption of the ingredient energy wave. The results revealed that the algorithm deployed in the process of encryption performed well. Simulations were performed in MATLAB.

Chaos-Based NMPC as a Novel MPPT Approach for Organıc Photovoltaıcs

Environmental degradation, alongside the dire consequences of climate change such as the melting of glaciers and rising sea levels, highlight the severe challenges associated with reliance on fossil fuels. As such, the shift towards sustainable and clean renewable energy sources, like photovoltaic systems, is becoming increasingly critical. This paper introduces a novel approach leveraging a chaotic-based nonlinear model predictive control to maximize the power output from organic photovoltaic cells. This method is distinguished by its rapid tracking capabilities and its effectiveness in enhancing the distribution network's performance under fault conditions. Utilizing a feedback-driven recursive control strategy, this approach efficiently predicts and adjusts to the optimal operating state, thereby minimizing its cost function. It comprises two primary phases: estimating the reference point and subsequently adjusting the operating point in alignment with this reference. In this process, the Lagrange function plays a pivotal role in optimizing the estimator's performance, while a chaotic neural network model predictive controller manages the boost converter's operation. Implementing this chaos-based nonlinear model predictive controller has successfully reduced overvoltage incidents by more than 1.3%. Notably, in the absence of such control methods, the penetration of OPV panels leads to voltage fluctuations beyond acceptable limits. The findings demonstrate that, alongside a decrease in network losses, there is an increase in the capacity of distribution feeders and a notable enhancement in the system's overall efficiency.

Dynamical behavior of a new jerk system inspired from chaotic memory oscillators

This paper constructs a six-term new simple 3D jerk system modeled by chaotic model memory oscillators with four parameters that control the behavior. The suitable choice of one of these parameters helps the system describe behavior and attractors. This means that the choice is a parameter of the associated behavior (dissipative or conservative) and attractors (self-excited or hidden). Some features of the equilibrium are observed that are related to the dependence on these parameters, such as saddle-foci, non-hyperbolic, and node-foci. This system is rich in dynamic features including chaotic, quasi-periodic (2-torus), and periodic via the utilization of bifurcation diagrams and Lyapunov spectrum. Finally, a new image encryption algorithm is introduced that utilizes the jerk system. The algorithm is assessed through statistical performance analysis, according to the results of the experiments and security tests, it has been verified that the suggested image encryption algorithm is highly secure and could be a viable option for real-world applications.

Coherent Chaotic Communication Using Generalized Runge–Kutta Method

Computer simulation of continuous chaotic systems is usually performed using numerical methods. The discretization may introduce new properties into finite-difference models compared to their continuous prototypes and can therefore lead to new types of dynamical behavior exhibited by discrete chaotic systems. It is known that one can control the dynamics of a discrete system using a special class of integration methods. One of the applications of such a phenomenon is chaos-based communication systems, which have recently attracted attention due to their high covertness and broadband transmission capability. Proper modulation of chaotic carrier signals is one of the key problems in chaos-based communication system design. It is challenging to modulate and demodulate a chaotic signal in the same way as a conventional signal due to its noise-like shape and broadband characteristics. Therefore, the development of new modulation–demodulation techniques is of great interest in the field. One possible approach here is to use adaptive numerical integration, which allows control of the properties of the finite-difference chaotic model. In this study, we describe a novel modulation technique for chaos-based communication systems based on generalized explicit second-order Runge–Kutta methods. We use a specially designed test bench to evaluate the efficiency of the proposed modulation method and compare it with state-of-the-art solutions. Experimental results show that the proposed modulation technique outperforms the conventional parametric modulation method in both coverage and noise immunity. The obtained results can be efficiently applied to the design of advanced chaos-based communication systems as well as being used to improve existing architectures.

On Mechanical and Chaotic Problem Modeling and Numerical Simulation Using Electric Networks

After reviewing the use of electrical circuit elements to model dynamic processes or the operation of devices or equipment, both in real laboratory implementations and through ideal circuits implemented in simulation software, a network model design protocol is proposed. This approach, following the basic rules of circuit theory, makes use of controlled generators to implement any type of nonlinearity contained in the governing equations. Such a protocol constitutes an interesting educational tool that makes it possible for nonexpert students in mathematics to design and numerically simulate complex physical processes. Three applications to mechanical and chaotic problems are presented to illustrate the versatility of the proposed protocol.

Alignments in the orientation of radio jets from AGN and their host galaxies

It is well established that active galactic nuclei (AGNs) play an important role in the evolution of galaxies. These AGNs can be linked to the accretion processes onto massive black holes and past merger events in their host galaxies, which may lead to different alignments of the jets with respect to the host galaxies. This paper presents a study of the position angle (PA) differences between radio and optical images of radio-AGNs based on the second data release (DR2) of the Low Frequency Array (LOFAR) Two-Meter Sky Survey (LoTSS), the Karl G. Jansky Very Large Array Faint Images of the Radio Sky at Twenty-Centimeters Survey (FIRST), the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys, and the Sloan Digital Sky Survey (SDSS). We assessed PA measurement biases in the data and classified the radio-AGNs based on the radio luminosity and infrared colour from the Wide-field Infrared Survey Explorer (WISE). This resulted in the largest sample of radio AGNs with reliable radio and optical PA measurements published to date, with a total of 3682 AGNs. The PA difference (dPA) distributions for the radio-AGN sample show a prominent minor-axis alignment tendency. Based on some simple assumptions, we simulated the projection effect to estimate the intrinsic jet--galaxy alignment. The observed dPA distribution can be well described by a two-component jet-alignment model in which one component is more aligned with the minor axis of the host galaxy than the other. The fitting results indicate that the jet alignment is dependent on radio luminosity and the shape of the host galaxies, with the jets being more likely to be aligned with the minor axis of the galaxy for lower radio luminosity and for optically more elongated radio-AGNs. The minor-axis alignment of the entire sample may suggest a coherent accretion model present in most AGN host galaxies, while a considerable number of luminous radio-AGNs with massive host galaxies might have undergone accretion ---according to the chaotic model--- or past merger events.

An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images.

The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the shortcomings of current chaotic systems, an n-dimensional cosine-transform-based chaotic system (nD-CTBCS) with a chaotic coupling model is suggested in this study. To create chaotic maps of any desired dimension, nD-CTBCS can take advantage of already-existing 1D chaotic maps as seed chaotic maps. Three two-dimensional chaotic maps are provided as examples to illustrate the impact. The findings of the evaluation and experiments demonstrate that the newly created chaotic maps function better, have broader chaotic intervals, and display hyperchaotic behavior. To further demonstrate the practicability of nD-CTBCS, a reversible data hiding scheme is proposed for the secure communication of medical images. The experimental results show that the proposed method has higher security than the existing methods.

Chaotic model and control of an atmospheric convective system coupled with large-scale circulation

Large-scale weather systems affect or determine the generation, development and movement of small- and medium-scale convective weather systems, and the understanding of their influence mechanism is of great significance for the prediction and forecasting of small- and medium-scale convective systems. From the perspective of dynamics, based on the Lorenz–Stenflo model describing convective systems and the Lorenz84 model describing low-order atmospheric circulation, we constructed a chaotic model of an atmospheric convective system considering large-scale circulation, analyzed the influence of the system parameters on the convective system, and designed a state feedback controller to adjust the convective motion. For the constructed convective weather system model, the existence and boundedness of its solution were analyzed, the Hamiltonian quantity was solved, the dynamic characteristics of the Lyapunov exponent, bifurcation diagram, attractor phase diagram and other methods were used to analyze its dynamic characteristics, the physical significance of its dynamic behavior was discussed, and the influence mechanism of the system parameters on convective weather was given. Additionally, the temperature difference between the upper and lower air currents is changed by the state feedback method, which provides a feasible scheme for adjusting the intensity of convective motion. The simulation experiments show that the chaotic model can explain and reveal the complex dynamic behavior of large-scale weather circulation in small- and medium-scale convective systems, which is of great significance for improving the prediction accuracy of convective systems in local areas, and feedback control can obtain the desired convective motion state.

Chaos and localized phases in a two-body linear kicked rotor system.

Despite the periodic kicks, a linear kicked rotor (LKR) is an integrable and exactly solvable model in which the kinetic energy term is linear in momentum. It was recently shown that spatially interacting LKRs are also integrable, and results in dynamical localization in the corresponding quantum regime. Similar localized phases exist in other nonintegrable models such as the coupled relativistic kicked rotors. This work, using a two-body LKR, demonstrates two main results; first, it is shown that chaos can be induced in the integrable linear kicked rotor through interactions between the momenta of rotors. An analytical estimate of its Lyapunov exponent is obtained. Second, the quantum dynamics of this chaotic model, upon variation of kicking and interaction strengths, is shown to exhibit a variety of phases: classically induced localization, dynamical localization, subdiffusive, and diffusive phases. We point out the signatures of these phases from the perspective of entanglement production in this system. By defining an effective Hilbert space dimension, the entanglement growth rate can be understood using appropriate random matrix averages.

Explaining the Stylized Facts of Foreign Exchange Markets with a Simple Agent-based Version of Paul de Grauwe’s Chaotic Exchange Rate Model

AbstractWe propose a simple agent-based version of Paul de Grauwe’s chaotic exchange rate model. In particular, we assume that each speculator follows his own technical and fundamental trading rule. Moreover, a speculator’s choice between these two trading philosophies depends on his individual assessment of current market circumstances. Our agent-based model setup is able to explain a number of important stylized facts of foreign exchange markets, including bubbles and crashes, excess volatility, fat-tailed return distributions, serially uncorrelated returns and volatility clustering. A stability and bifurcation analysis of its deterministic skeleton provides us with useful insights that foster our understanding of exchange rate dynamics.