Results in Nonlinear Analysis

An information analysis of a novel fractional chaotic systems and its application to image encryption

2025-08-11T10:09:47+03:00

This paper introduces a new class of fractional chaotic systems with no fixed points, corresponding to standard chaotic maps, which exhibit chaotic behavior. We show the relationships between entropy in information theory and intrinsic properties in chaos theory of the proposed system. The chaotic behavior of this class is analyzed by exploring numerically using phase plots, bifurcation diagrams, Lyapunov exponents, and approximate entropy to examine the dynamics of the designed system and assess the effectiveness of varying the fractional order. An exact expression for solutions of the system is determined. Additionally, a new chaotic attractor is presented. In the practical aspect of this work, we present an image encryption algorithm based on the proposed system. Based on the experimental results obtained, we can conclude that the proposed algorithm achieves effective encryption with enhanced security, making it resistant to common attacks.

Marcinkiewicz functions on product spaces along surfaces of revolution

2025-08-25T18:56:18+03:00

In this paper, specific Lp bounds for a class of Marcinkiewicz integral operators on product spaces along surfaces of revolution are established whenever the kernel functions are rough in Lq n m ( ) 1 1   . By virtue of the obtained bounds and an extrapolation argument, we prove that the aforementioned operators are bounded on Lp n m ( )  × under rather weaker conditions on the kernel functions. The results in this work represent essential improvements and extensions of several results on Marcinkiewicz operators.

Hybrid Quantum–Cloud Framework for Nonlinear Clustering Optimization and Intelligent Resource Management

2025-09-30T12:49:29+03:00

This paper proposes a hybrid quantum-cloud computing architecture, which ought to be applied to overcome the two problems of nonlinear clustering optimization and intelligent management of large-scale resources in the heterogeneous environments. The current cloud workloads in terms of complexity, scalability, and energy needs are not always easily met by the conventional machine learning and heuristic scheduling processes, particularly in cases where the data possess nonlinear structures. These weaknesses will be mitigated by the proposed framework that will integrate quantum-inspired algorithms (which will operate on variational quantum circuits and Quantum Approximate Optimization Algorithm (QAOA)) with cloud-native orchestration solutions, only that reinforcement learning-based scheduling will be integrated. This architecture has its quantum layer where nonlinear clustering is done to achieve more accurate workload partitioning, and cloud layer sharing resources and balancing throughput, latency, and energy efficiency. It is a broker interface that provides a fluent communication between quantum processors and cloud infrastructure that makes it possible to make real time decisions. The synthetic nonlinear clustering, IoT workloads and big data traces benchmark datasets were experimentally simulated on CloudSim and Kubernetes. Results indicate that the framework can lead to a significant performance increase as compared to conventional approaches and that the accuracy of the clustering process has been enhanced by 12-18, average job latency has been reduced by 22 and resource utilization efficiency has been improved by 25. Additionally, the hybrid approach is very scalable and stable as the degree of workload varies and is able to support quality-of-service (QoS) even during the peak period of workload. In these studies, the findings show the possibility of quantum and cloud computing hybridization to the next generation of intelligent cloud eco-systems to give a pathway to green, flexible, and high-performance computing in the current areas, 6G networks, smart cities, bioinformatics, and smart financial analytics.

AI-driven nonlinear optimization for knowledge extraction and pattern analysis in IoT-enabled data mining systems

2025-09-30T12:37:15+03:00

In this paper, systematic exploration of the application of AI-based nonlinear optimization to elicit knowledge and pattern study in the IoT-enabled data mining takes place. The paper explains the complexity and heterogeneity of IoT data on scale by declaring and resolving nonlinear optimization problems using the latest AI methods, including genetic algorithms and neural networks. On smart grid, city traffic, and industrial data, a modular computing framework is constructed consisting of fog computing over edges, cloud storage and embedded AI engines. The result of the experiment is that nonlinear optimization algorithms are better than the classical linear and clustering algorithms in accuracy and effectiveness, which tells of the presence of multi-layered latent structures that are significant in the analytics of IoT. The paper lists the advantages of the nonlinear complexities of determining the actionable patterns then outlines the outlooks of the future development of multi-objective modeling, federated learning, and privacy-respectful analytics in dynamic IoT environments.

Data visualization and pattern discovery in IoT: a nonlinear optimization and AI-based knowledge extraction approach

2025-09-30T12:43:34+03:00

The fast multiplication of Internet of Things (IoT) ecosystems has led to huge amounts of heterogeneous, high-dimensional, and dynamic data, which are difficult to analyze and make decisions. Traditional linear visualization and analysis tools are also not always suitable to show the nonlinear correlations, latent dependencies, and changing patterns in IoT data. This paper attempts to fill this gap by presenting a holistic nonlinear optimization and artificial intelligence (AI)-supported framework of IoT data visualization and pattern discovery. The given method is a combination of nonlinear optimization of features with the help of metaheuristic algorithms and sophisticated dimensionality reduction techniques to preserve the important information with reducing redundancy. The knowledge, anomalies, and predictive trends in sensor networks are then extracted, detected, and identified using AI-driven models such as deep neural networks, graph neural networks, and reinforcement learning agents. An interpretable visualization layer that is trained on manifold learning methods like UMAP is more interpretable since the optimized feature spaces are then mapped to low-dimensional human-readable visual representations. The framework is proven by case-studies of smart agriculture and industrial IoT that prove the framework effective in optimization of irrigation schemes, enhancing crop yield forecasting, facilitating early fault detection, and minimizing downtime in production systems. The results of experiments indicate that it is more accurate, separates clusters better and that it is less complex to compute in comparison to the conventional methods to linear analysis like PCA and k-means clustering. The results highlight the disruptive nature of AI-enhanced nonlinear optimization to fill the gap between raw IoT data and actionable knowledge and thus provide scalable, interpretable, and intelligent analytics to next-generation IoT enabled applications.

A comprehensive extended SEIR model for hMPV transmission: Integrating co-infection and vaccination dynamics for Türkiye’s model

2025-09-04T09:34:08+03:00

Human metapneumovirus (hMPV) is a common respiratory virus that represents a major public health burden, especially in children, older adults, and immunocompromised patients. However, traditional compartmental models, which apply to single-pathogen transmission, do not always adequately characterize the complexity of co-infections and vaccination dynamics. Here, we extend a SEIR model with two more compartments: one for those coinfected with hMPV, one for those infected with respiratory viruses other than hMPV, and another compartment for the vaccinated. This complex frame allows a realistic representation of hMPV transmission and control interventions. As a numerical solution method, we use the finite difference method (FDM) to study the behavior of these nonlinear and coupled differential equations. This method breaks down the time evolution of each compartment and can be used to simulate disease dynamics under different public health intervention schemes, such as vaccination rates. Simulation shows that intensive vaccination would significantly decrease the peak of infections and expedite the epidemic's control, especially together with non-pharmaceutical interventions. The co-infection compartment shows how the simultaneous presence of overlapping infections can exacerbate the severity of an epidemic, emphasizing the need for combined control strategies. Our model is a useful tool for understanding hMPV epidemic in the presence of other pathogens, which helps estimate the efficacy of vaccination strategies. This biologically motivated model, coupled with a strong numerical solution, provides important information for health authorities in their quest to minimize the effects of the disease.

Non linear clustering optimization for scalable data mining in cloud and quantum computing environments

2025-09-30T12:59:58+03:00

The article outlines an optimization model of nonlinear clustering that could strike a balance between the use of the complex mathematical models and scalability to the cloud and quantum computing systems. It is based on the classical clustering methodology, but utilizes nonlinear objective functions, graph, and manifold-sensitive regularization, and explicit resource constraints to find the subtle, non-Euclidean structures in heterogeneous data. The approach combines the dynamical systems analysis, PDE-based manifold models and quantum optimization mappings (QUBO/Ising), which ensure the theoretical soundness of the approach; specifically, the approach is coercive, has minimizers, and block-coordinate convergence guarantees. The system architecture makes use of the hybrid cloud-quantum orchestration, in which the workload clustering will dynamically relocate to distributed classical resources and quantum processors to optimize time, memory, power, and qubit usage. Evolutionary search also has adaptability, and neural feature embedding, as well as quantum solvers, are used to improve adaptability. Discrete assignment optimization under hardware-friendly penalties. These large-scale studies of synthetic manifolds, high-dimensional benchmarking, and real-world benchmarking reveal a much higher clustering accuracy, scaling, and resource efficiency than k-means, spectral clustering, and kernel methods, and density-based baselines. Ablation experiments prove the role of each nonlinear and quantum-inspired element and transparency protocols are made with regard to cloud and QPU systems. The findings make nonlinear analysis a fundamental component of unsupervised learning in the present day, and apply to the dynamical systems modelling, interpretable data mining, and resource-sensitive algorithm design. The model offers an intellectual roadmap to the future of cloud-quantum clustering systems that will take into account the needs of engineering, scientific, and industrial discovery.

On certain properties of functions associated with a nonlinear operator

2025-06-12T10:36:47+03:00

In this article, we develop a nonlinear operator $\mathfrak{\Im}%

_{\alpha,\gamma}^{\sigma}\left( f\right) \left( z\right) :$%

\[

\mathfrak{\Im}_{\alpha,\gamma}^{\sigma}\left( h\right) \left( z\right)

:=\left( 1-\alpha \right) \sigma+\alpha \phi \left( z\right) -\frac{\gamma

z\phi^{\prime}\left( z\right) }{\phi \left( z\right) }-\left(

1-\alpha-\gamma \right) \frac{z\left( \phi \left( z\right) +z\phi^{\prime

}\left( z\right) \right) ^{\prime}}{\phi \left( z\right) +z\phi^{\prime

}\left( z\right) },

\]

based on the functional $\phi \left( z\right) :=\left( \frac{z}{f\left(

z\right) }\right) ^{\sigma}f^{\prime}\left( z\right) :z\in \mathbb{E},$ the

open unit disk, $\alpha,\gamma \in \mathbb{R},$ $\sigma \in \left[ -1,1\right] $

\ and find conditions on the functional $\left( \frac{z}{f\left( z\right)

}\right) ^{\sigma}f^{\prime}\left( z\right) $ so that it is a filtration.

Moreover, we define a family $\mathcal{R}_{\sigma}\left( \alpha

,\gamma \right) $ and study bounds on Fekete-Szeg\"{o} functional $%

%TCIMACRO{\tciFourier}%

%BeginExpansion

\mathcal{F}%

%EndExpansion

_{f}\left( \eta \right) $ along with some inclusions and different related

results. These results can be further extended to symmetric, conjugate

symmetric and other related setting in the present formulations.

Geometric application of a viscosity approximation- type iterative method to the generation the fractals as Julia and Mandelbrot Sets for complex function

2025-10-09T13:15:46+03:00

This work explores an application of novel fractal patterns, specifically Julia and Mandelbrot sets, generated by a modified class of complex function in which the traditional constant term is replaced with a logarithmic function. Utilizing a viscosity approximation-type iterative method, we develop escape criteria that enhance existing algorithms, thereby enabling the precise visualization of intricate fractal structures as Julia and Mandelbrot sets. Numerical experiments in MATLAB reveal that varying the input parameters induces significant dynamic transformations in the fractals’ morphol-
ogy. We believe that the insights gained from this study will inspire and motivate researchers and enthusiasts with a deep interest in fractal geometry.

Image compression technique based on two new parametrized thresholding operators

2025-09-18T09:45:25+03:00

In this paper, we introduce a new way to compress images using two innovative thresholding operators that are carefully designed with parameters. These operators are meant to handle comparison tasks more effectively. Our results show that they have clear benefits and perform better than the usual Hard and Soft thresholding methods. We’ve also included some example images and data to show how accurate and efficient our approach is, especially when looking at PSNR and CR measurements.

Application of parametric technique in solving linear Neutrosophic partial differential-algebraic controlled Systems with index-3

2025-12-17T10:26:16+03:00

The current study presents and verifies a new method for solving Neutrosophic Differential-algebraic Controlled Systems with index-3. The method uses the critical point of the formulated Neutrosophic Partial Differential-algebraic variational formulation with Neutrosophic consistent initial condition to be solution for the proposed system and via-versa. With help of differentiation index with respect to time, the reduced constrained control problem in the state-space is then obtained. This transforms variational problem from indirect method into direct method by the technique of generalized Ritz bases. Finally, battery model numerical results confirm the results of the theory.

AI-Driven Nonlinear Optimization Model for Early Lung Tumor Growth Prediction Using CT Imaging and Machine Learning Algorithms

2025-12-26T17:04:35+03:00

The timely detection of lung tumour development is important in the planning of individual therapy and enhancing survival. Although deep learning models have demonstrated good performance in tumour analysis based on CT, their low interpretability inhibits their integration in clinical practise. This paper presents a hybrid using AI and nonlinear tumour growth modelling and machine learning optimisation to forecast the initial progression of lung tumours based on CT scan data. The growth model of a nonlinear set of nonlinear differential equations (Gompertz /logistic) is fitted by first constrained nonlinear optimization on the sequential tumour volumes. The estimated parameters are the growth rate (r), carrying capacity (K), as well as the deceleration factor, then they are incorporated into a deep convolutional network, which will be trained to predict tumour size at subsequent time points. A longitudinal CT dataset of lung cancer patients at an early stage (N = 52) was experimented on to show that the hybrid model reduced prediction RMSE to 4.23 cm³, which was better than base line CNN-only and purely mechanistic models by 45.9% and 34.0% respectively. There was also a significant correlation between growth parameters and clinical progression (p < 0.01) thus increasing the interpretability of the models. The suggested framework is efficient in closing the gap between mechanistic nonlinear modelling and current deep learning and leads to robust, interpretable, and clinically meaningful predictions of tumour growth

Machine Learning-Integrated PDE Model for Blood Flow Simulation and Arterial Plaque Progression Detection in Cardiovascular Diagnosis

2025-12-26T17:11:51+03:00

The main issues in the modern cardiovascular diagnosis are the accurate prediction of the blood flow dynamics and the possibility to identify the arterial plaque progression at the initial stage. Partial differential equations (PDE)-based traditional computational fluid dynamics (CFD) models, especially the Navier-Stokes equations, provide high-fidelity hemodynamic models, but are expensive and demand considerable computational power and cannot be readily adapted to patient pathophysiological variations. Machine learning (ML) on the other hand, is good at real-time inference, but is not always interpretable and physically consistent. The paper provides a hybrid ML-based PDE model, which integrates physics-based modelling and learned surrogate modules to speed up the process of simulation, improve prediction of plaque-progression, and be physiological-valid. The ML model was trained on a dataset of coronary artery CT scans and Doppler ultrasound measurements and the PDE-based solver was validated. The hybrid method was better at prediction and 20 times less costly in computational cost compared to classical solvers. All the statistics and tables that are mentioned in the text are presented in the article.

Artificial Intelligence-Based Nonlinear Mathematical Modeling and Control of Glucose-Insulin Dynamics in Type 2 Diabetic Patients

2025-12-26T17:15:43+03:00

The relationship between glucose and insulin regulation in type 2 diabetes mellitus (T2DM) is non-linear and highly dynamic and cannot be dealt with by exact modelling and smart control. The proposed study is a combination of artificial intelligence (AI)-based nonlinear mathematical modelling and control in addressing glucose insulin dynamics in diabetic patients with type 2 diabetes (T2DM). It begins with the construction of a nonlinear physiological model based on lengthy principles of minimal modelling of Bergman of the absorption of glucose into the body and the secretion of insulin and peripheral uptake in the face of pathological insulin resistance. Machine learning-based adaptive estimators are also used to further optimise the model parameters in capturing the inter-individual physiological variability. Subsequently, a hybrid type of control that involves both model predictive control (MPC) and reinforcement learning (RL) is created to control exogenous insulin delivery in the face of meals and metabolic disturbances. The results of the simulation prove that the system proposed will have a much higher level of glucose regulation, less postprandial hyperglycemia, and a stronger response to parameter uncertainty than the traditional proportional-integral-derivative (PID) and classical MPC plans. The AI-enhanced model predicts the glucose kinetics accurately and it attains a stable control without causing the hypoglycemia. The results demonstrate how AI-based nonlinear models can be effective in aiding patient-specific closed-loop insulin therapy and that this can provide a viable direction toward real-time individualized diabetes treatment.

Deep Learning and Nonlinear Optimization-Assisted PDE Segmentation Framework for Accurate Brain Tumor Boundary Detection in MRI Scans

2025-12-26T17:19:50+03:00

The correct outline of the brain tumour in magnetic resonance imaging (MRI) is an essential process in the neurosurgical planning process, radiation therapy, and longitudinal monitoring. The framework suggested in this paper combines deep learning with nonlinear partial differential equation (PDE)–based optimization in high-precision tumour boundary segmentation of multi-modal MRI scans. A convolutional neural network (CNN) is initially trained to give an initial approximate tumour and neighboring edema tissues segmentation mask. Second, a level-set module is a PDE-based level-set module, which is driven by nonlinear energy minimization, to refine the boundary, hence imposing smoothness and retaining fine structural information. The optimization parameters are adjusted in an adaptive manner by a deep reinforcement learning optimizer to learn control policies of the PDE energy weights to allow capturing patient-specific variability. Extensive trial on publicly accessible multi-modal MRI brain tumor datasets reveal that the framework proposed achieves significant enhancement in Dice similarity coefficient (DSC) increase of 4.7percent as well as decreased 95th-percentile Hausdorff distance (HD95) relative to state-of-the-art deep-learning segmentation on its own. Corrupted input and missing modality robustness tests demonstrate little performance drop (DSC decline less than 1.8 percent). This shows that the combination of deep learning and nonlinear optimization can be used to successfully present accurate and clinically reliable brain tumour boundary detection.

Fully Implicit Differences Method for Solving Couple Parabolic System with Variable Coefficients

2025-12-01T11:51:51+03:00

This article concerns with introducing new technique to solve a new type of PDE described by coupled parabolic system with variable coefficients (CPSVC) by utilizing the fully finite implicit differences method (FFIDM). At each discrete value of time the proposed technique is used to transform the CPSVC into a couple linear algebraic system (CLS) that they are solved using the Gauss elimination method (GEM) to get the numerical couple solution (NCS) for the problem. The consistency of the method is studied so as the stability. Some examples are given and the results are described by tables and figures to illustrate the accuracy for the proposed technique, it is concluded that this method is accurate and suitable for solving such systems