Results in Nonlinear Analysis

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

Adil Khudhair Bagheedh — 2025-10-21

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

Mohammed Ali — 2025-10-21

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

R.Indhumathi — 2025-10-18

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

S.Pandikumar — 2025-10-22

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

K.Nandha Kumar — 2025-10-22

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

Aytekin Enver — 2025-10-22

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

S Manjula — 2025-10-24

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.

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

Iqbal Ahmad — 2025-10-28

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.