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Examining finite-time behaviors in the fractional Gray–Scott model: Stability, synchronization, and simulation analysis

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International Journal of Cognitive Computing in Engineering 2025年 6卷 380-390页

作者： Momani, Shaher Batiha, Iqbal M. Bendib, Issam Ouannas, Adel Hioual, Amel Mohamed, Dalah Department of Mathematics Faculty of Science The University of Jordan Amman11942 Jordan Ajman University Ajman United Arab Emirates Department of Mathematics Al Zaytoonah University of Jordan Amman11733 Jordan Applied Mathematics & Modeling Laboratory Department of Mathematics Faculty of Exact Sciences University of Brothers Mentouri Constantine25000 Algeria Department of Mathematics and Computer Science University of Oum El Bouaghi Oum El Bouaghi04000 Algeria

This paper investigates the behavior and stability of the fractional-order Gray–Scott model, with a specific focus on achieving finite-time stability and synchronization. It introduces essential concepts, including the Gamma function, the Riemann–Liouville fractional-order integral operator, the Caputo fractional derivative, and the Mittag-Leffler function, to establish a foundational framework for subsequent analysis. Equilibrium points are defined, distinguishing between initial and finite-time equilibria, and the conditions for finite-time stability, including settling time, are precisely outlined. Stability results for this model are presented through theorems with detailed proofs, elucidating the roles of Lyapunov functions, class functions, and other system parameters. Furthermore, the paper explores finite-time synchronization schemes in master–slave systems, providing a mathematical framework for understanding and achieving synchronization within a finite time frame. This framework illuminates synchronization dynamics and their practical implications for controlling complex systems. Additionally, numerical examples illustrate finite-time stability and synchronization within the Gray–Scott reaction–diffusion model. © 2025 The Authors

关键词： Lyapunov functions

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Enhancing photovoltaic energy forecasting:a progressive approach using wavelet packet decomposition

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Clean Energy 2024年第3期8卷 95-108页

作者： Khaled Ferkous Mawloud Guermoui Abderahmane Bellaour Tayeb boulmaiz Nadjem Bailek LMTESE Laboratory of Materials Technology of Energy Systems and EnvironmentUniversitéde Ghardaia47000Algeria Renewable Energy Applied Research Unit(URAER) Ghardaia47000Algeria Laboratory of Mathematics Modeling and Applications Department of Mathematics and Computer ScienceFaculty of Sciences and TechnologyAhmed Draia University of AdrarAdrar 01000Algeria

Accurate photovoltaic(PV)energy forecasting plays a crucial role in the efficient operation of PV power *** study presents a novel hybrid machine-learning(ML)model that combines Gaussian process regression with wavelet packet decomposition to forecast PV power half an hour *** proposed technique was applied to the PV energy database of a station located in Algeria and its performance was compared to that of traditional forecasting *** evaluations demonstrate the superiority of the proposed approach over conventional ML methods,including Gaussian process regression,extreme learning machines,artificial neural networks and support vector machines,across all *** proposed model exhibits lower normalized root mean square error(nRMSE)(2.116%)and root mean square error(RMSE)(208.233 kW)values,along with a higher coefficient of determination(R^(2))of 99.881%.Furthermore,the exceptional performance of the model is maintained even when tested with various prediction ***,as the forecast horizon extends from 1.5 to 5.5 hours,the prediction accuracy decreases,evident by the increase in the RMSE(710.839 kW)and nRMSE(7.276%),and a decrease in R2(98.462%).Comparative analysis with recent studies reveals that our approach consistently delivers competitive or superior *** study provides empirical evidence supporting the effectiveness of the proposed hybrid ML model,suggesting its potential as a reliable tool for enhancing PV power forecasting accuracy,thereby contributing to more efficient grid management.

关键词： short photovoltaic power forecasting wavelet packet decomposition sub-series reconstruction machine learning in energy forecasting sustainable power stations renewable energy

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On Elliptic Pseudo-differential Equations with an Integral Condition in a Special Multidimensional Cone

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Lobachevskii Journal of mathematics 2024年第11期45卷 5487-5496页

作者： Gebreslasie, Hadish Fessehatsion Vasilyev, Vladimir B. Department of Applied Mathematics and Computer Modeling Belgorod State National Research University Belgorod 308015 Russian Federation Mainefhi College of Science National Higher Education and Research Institute Asmara 12676 Eritrea

Abstract: In this paper, one considers a model pseudo-differential equation in five-dimensional space outside of a cone like multi-faced angle. Using the wave factorization of elliptic symbol one constructs a general solution of the equation, and it depends on one arbitrary function from corresponding Sobolev–Slobodetskii space. One adds a certain integral condition to the equation for unique identification of this function. One studies a solvability for this problem when certain parameters of the cone tend to their limit values. © Pleiades Publishing, Ltd. 2024.

关键词： asymptotic behavior of solution general solution integral condition pseudo-differential equation wave factorization

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Sequential Solution Strategies for the Cahn-Hilliard-Biot Model

Sequential Solution Strategies for the Cahn-Hilliard-Biot ...

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European Conference on Numerical mathematics and Advanced Applications, ENUMATH 2023

作者： Storvik, Erlend Riethmüller, Cedric Both, Jakub W. Radu, Florin Adrian Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Bergen Norway Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany Centre for Modeling of Coupled Subsurface Dynamics Department of Mathematics University of Bergen Bergen Norway

ISBN: (纸本)9783031861680

This paper presents a study of solution strategies for the Cahn-Hilliard-Biot equations, a complex mathematical model for understanding flow in deformable porous media with changing solid phases. Solving the Cahn-Hilliard-Biot system poses significant challenges due to its coupled, nonlinear and non-convex nature. We explore various solution algorithms, comparing monolithic and splitting strategies, focusing on both their computational efficiency and robustness. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Computational efficiency

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On One Method for Choosing the Planned Trajectory of Parallel Multi-Link Manipulators as Mechatronic Systems with Geometric Constraints

On One Method for Choosing the Planned Trajectory of Paralle...

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2023 International Russian Automation Conference, RusAutoCon 2023

作者： Krasinskiy, Aleksandr Ya. Yuldashev, Andrey Scientific Department of Rosbiotech Dept. of Computer Modeling and Probability Theory Moscow Russia Faculty Number 8 Information Technology and Applied Mathematics Moscow Russia

ISBN: (纸本)9798350345551

Robotic manipulators, as the most versatile class of modern automatic devices, are part of most automated production systems. The versatility of robots is largely associated with the developed software of the controllers included in their composition. However, despite certain achievements, there are no sufficiently effective commercial software products that solve the problem of planning the trajectories of multilink manipulators. The problem of trajectory planning acquires particular complexity for organizing the joint work of several manipulators, which is relevant for engineering practice: in order to avoid collisions, it is necessary to control the trajectory not only of the working body, but also of all nodes of each manipulator. In view of the obvious ambiguity for the solution of the inverse kinematics problem, necessary for planning, it is necessary to introduce some criteria that exclude ambiguity. In this paper, we discuss the possibility for applying the methods of analytical mechanics to implement the proposed approach - the choice of a trajectory based on the minimum energy consumption along the planned trajectory. © 2023 IEEE.

关键词： Trajectories

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Analysis of Nonlinear Processes in the P-I-N Diodes Plasma by the Perturbation Theory Methods 13

Analysis of Nonlinear Processes in the P-I-N Diodes Plasma b...

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13th International Conference on Advanced computer Information Technologies, ACIT 2023

作者： Bomba, Andrii Moroz, Igor National University of Water and Environmental Engineering Department of Computer Science and Applied Mathematics Rivne Ukraine Rivne State University of Humanities Department of Information Technologies and Modeling Rivne Ukraine

A nonlinear singularly perturbed boundary value problem of the electron-hole plasma state predicting in the p-i-n diodes active region is considered. The search for solutions to the problem is carried out by the asymptotic method of boundary corrections. The decomposition of the original problem is carried out, the results are analyzed, and the existence of its asymptotic solutions is proved. © 2023 IEEE.

关键词： Plasma diodes

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On the Security Related Properties of Randomly Constructed Combinatorial Structures 8th

On the Security Related Properties of Randomly Constructed...

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8th International Symposium on Cyber Security, Cryptology, and Machine Learning, CSCML 2024

作者： Liagkou, V. Nastou, P.E. Spirakis, P. Stamatiou, Y.C. Computer Technology Institute and Press - "Diophantus" University of Patras Campus Patras26504 Greece Department of Computer Science University of Liverpool Liverpool United Kingdom Department of Business Administration University of Patras Patras26504 Greece Department of Informatics and Telecommunications University of Ioannina Koatakioi Arta47100 Greece Department of Mathematics Applied Mathematics and Mathematical Modeling Laboratory University of the Aegean Samos Greece

ISBN: (纸本)9783031769337

This paper explores the interplay between randomly generated structures, namely set families as well as second-order logic 0-1 laws, in security-related settings. The paper investigates how randomly generated structures can serve as powerful models for representing security properties of complex systems. By examining the 0-1 properties of these structures, conditions are stated which determine the presence or absence of specific security issues. The stated results provide a generic framework for studying insights into the probabilistic behavior of security attributes modeled by set families and mathematical logic with application potential in designing more robust systems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： computer circuits

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Semi-analytical finite element method applied for characterizing micropolar fibrous composites

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applied mathematics and Mechanics(English Edition) 2024年第12期45卷 2147-2164页

作者： J.A.OTERO Y.ESPINOSA-ALMEYDA R.RODRIGUEZ-RAMOS J.MERODIO School of Engineering and Sciences Monterrey Institute of TechnologyEstado de Mexico 52926Mexico Institute of Engineering and Technology Autonomous University of Ciudad JuarezCiudad JuarezChihuahua 32310Mexico Postgraduate Program in Computational Modeling in Science and Technology Federal Fluminense UniversityRıo de Janeiro 27255-125Brazil Faculty of Mathematics and Computer Science University of HavanaLa Habana 10400Cuba Department of Mathematics Applied to ICT School of Informatics Systems EngineeringTechnical University of MadridMadrid 28031Spain

A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous *** framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact *** mathematical formulation of the local problems and the effective coefficients are presented by the *** local problems obtained from the AHM are solved by the FEM,which is denoted as the *** numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.

关键词： semi-analytical approach fiber-reinforced composite(FRC) effective property finite element method(FEM) asymptotic homogenization method(AHM) micropolar elasticity

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To Heart via Liver: a Study on Prognostic Stratification of Heart Disease in MASLD Patients using Machine Learning Models 3

To Heart via Liver: a Study on Prognostic Stratification of ...

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3rd AIxIA Workshop on Artificial Intelligence For Healthcare, HC@AIxIA 2024

作者： Bruno, Pierangela Cirella, Antonio Di Cesare, Ernesto Greco, Gianluigi Guzzo, Antonella Palumbo, Pierpaolo Santini, Silvano Sinatti, Gaia Vittorini, Pierpaolo Calimeri, Francesco Balsano, Clara Department of Mathematics and Computer Science University of Calabria Rende Italy Department of Clinical Medicine Life Health & Environmental Sciences-MESVA University of L'Aquila Italy Department of Applied Clinical Sciences and Biotechnology University of L'Aquila Italy Department of Informatics Modeling Electronics and Systems Engineering University of Calabria Rende Italy

Accurate cardiovascular (CV) risk assessment is relevant for asymptomatic individuals, in particular for those at risk for cardiovascular diseases (CVD). Metabolic-associated fatty liver disease (MASLD), previously known as non-alcoholic fatty liver disease (NAFLD), is recognized as a critical independent risk factor for increased CV morbidity and mortality. With a prevalence of 25% in the general population, MASLD is the leading cause of chronic liver diseases and is strongly associated with the development of coronary artery disease (CAD). Coronary CT is widely used to detect CAD, and it can also assess liver steatosis, providing valuable prognostic information for at-risk patients. In this paper, we present a study on methods for performing prognostic stratification of CAD risk in asymptomatic MASLD patients using machine learning (ML) approaches. In particular, we conducted a retrospective analysis of clinical data from 60 patients who underwent Coronary CT at L'Aquila Hospital (Italy) between 2017 and 2021. Dataset includes significant features, such as radiodensity (Hounsfield Unit), calcium score (Agatston score), and liver fibrosis (Fib-4 score and APRI). We compared several ML algorithms (Logistic Regression, Support Vector Classifier (SVC), Random Forest, Extreme Gradient Boosting, K-Nearest Neighbors (KNN), Naive Bayes), with the main goal of performing binary classification tasks and creating a model able to differentiate between healthy patients and those affected by both MASLD and CVD. SVCs emerged as the best-performing models, achieving an AUC of 94%, an accuracy of 95%, and a recall of 94%. Our approach offers a robust and accurate tool for predicting CAD risk in MASLD patients, providing a valuable contribution to clinical practice for early CV risk stratification and management. © 2024 CEUR-WS. All rights reserved.

关键词： Risk assessment

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On the Existence of Highly Organized Communities in Networks of Locally Interacting Agents 7th

On the Existence of Highly Organized Communities in Netwo...

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7th International Symposium on Cyber Security, Cryptology, and Machine Learning, CSCML 2023

作者： Liagkou, Vasiliki Nastou, Panagiotis E. Spirakis, Paul Stamatiou, Yannis C. Computer Technology Institute and Press - "Diophantus" University of Patras Campus Patras26504 Greece Department of Computer Science University of Liverpool Liverpool United Kingdom Department of Business Administration University of Patras Patras26504 Greece Department of Informatics and Telecommunications University of Ioannina Kostakioi Arta47100 Greece Department of Mathematics Applied Mathematics and Mathematical Modeling Laboratory University of the Aegean Samos Greece Center for Applied Optimization University of Florida Gainesville United States

ISBN: (纸本)9783031346705

In this paper we investigate phenomena of emergence of highly organized structures in networks. Our approach is based on Kolmogorov complexity of networks viewed as finite size strings. We apply this approach to study the emergence of simple organized, hierarchical, structures based on Sierpinski Graphs and we prove a Ramsey type theorem that bounds the number of vertices in Kolmogorov random graphs that contain Sierpinski Graphs as subgraphs. Moreover, we show that Sierpinski Graphs encompass close-knit relationships among their vertices that facilitate fast spread and learning of information. In the context of our work we can investigate questions related to the emergence or formation of suitably large groups of malicious individuals in a networks of interacting agents, which are able to take control of the networks. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Graphic methods

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