Article
Mathematics, Interdisciplinary Applications
Adnene Arbi
Summary: This study investigates the exponential stability of monotone traveling wave solutions for a class of nonlinear delayed dynamical neural networks with leakage term and distributed delays. The new outcomes are obtained by applying Ikeharas theorem, the weighted energy method, Taylor formula, comparison principle, and the first integral mean value theorem. Additionally, the leakage term is considered for the first time in this work for the dynamical model of cellular neural networks.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Jason A. Platt, Stephen G. Penny, Timothy A. Smith, Tse-Chun Chen, Henry D. I. Abarbanel
Summary: Drawing on ergodic theory, this paper introduces a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The method enforces dynamical invariants in the systems, such as the Lyapunov exponent spectrum and the fractal dimension, which enables longer and more stable forecasts when operating with limited data. The technique is demonstrated using reservoir computing, a specific kind of recurrent neural network, and the effectiveness is verified with typical test cases.
Article
Computer Science, Artificial Intelligence
Ramazan Yazgan, Salsabil Hajjaji, Farouk Cherif
Summary: This work focuses on a nonlinear differential equation for a quaternion-valued recurrent neural network. The existence and global exponential stability of a weighted pseudo-almost automorphic solution for this type of neural network is directly studied using the contraction mapping principle and some differential inequalities. The methods used in this study do not involve a real or complex decomposition of the equation system. Additionally, an application and numerical simulation are provided to verify the results obtained. The generated results about the weighted pseudo-almost automorphic solution in the considered model are novel.
NEURAL PROCESSING LETTERS
(2023)
Article
Automation & Control Systems
Bing Li, Yuwei Cao, Yongkun Li
Summary: In this paper, a class of octonion-valued stochastic recurrent neural networks with time-varying delays is considered. The existence, uniqueness, and global exponential stability of almost automorphic solutions in distribution are proved using Banach fixed point theorem and inequality technique. The results obtained in this study are new. An illustrative example is also provided to demonstrate the effectiveness of the results.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2023)
Article
Engineering, Marine
Sachin Kumar, Amit Kumar
Summary: This paper investigates a nonlinear equation that describes fluid propagation and obtains the exact closed-form solutions using two efficient methods. These methods prove to be effective, authentic, and straightforward mathematical tools for obtaining closed-form solutions to nonlinear partial differential equations.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2022)
Article
Automation & Control Systems
Guang Ling, Xinzhi Liu, Ming-Feng Ge, Yonghong Wu
Summary: This paper investigates cluster synchronization of complex dynamical networks with noise and time-varying delays using a delayed pinning impulsive control scheme, establishing criteria to guarantee synchronization while revealing the relationship between performance and factors like impulsive input delays. The effectiveness of the theoretical results is demonstrated through numerical examples and computer simulations.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Automation & Control Systems
Xiaonan Liu, Minghui Song, Yonggui Kao
Summary: This paper investigates the synchronization between two hyperbolic coupled networks (HCNs) with time-varying delays using aperiodically intermittent pinning control (AIPC). Sufficient criteria for HCNs with internal delays only and with hybrid delays are obtained based on a Lyapunov function with a piecewise continuous function. It is found that HCNs with hybrid delays have a slower convergence speed compared to those with internal delays only. Additionally, two simulation results are presented to validate the theoretical findings.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Automation & Control Systems
Ning Zhang, Shunjie Huang, Wenxue Li
Summary: This paper investigates the pth moment exponential stability of stochastic delayed systems, taking into account both semi-Markov jumps and stochastic mixed impulses. It establishes new impulsive differential inequalities with semi-Markov jumps and stochastic mixed impulses. By cleverly combining graph theory, stochastic analysis techniques, and the Lyapunov method, stability criteria for stochastic delayed semi-Markov jump systems with stochastic mixed impulses are proposed. Finally, the theoretical results are applied to oscillator systems, and the simulation results confirm the effectiveness of the theoretical findings.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Peng Wan, Zhigang Zeng
Summary: This article analyzes the issue of global exponential stability for impulsive delayed neural networks on time scales by constructing impulse-dependent Lyapunov functionals and using timescale inequality techniques. The theoretical results derived from the timescale theory can be used to design impulsive control strategies to stabilize previously unstable delayed neural networks. The effectiveness and superiority of these results are demonstrated through numerical examples.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2022)
Article
Mathematics, Interdisciplinary Applications
Shang Gao, Keyu Peng, Chunrui Zhang
Summary: This paper presents a novel method to investigate the existence and global exponential stability of periodic solutions for feedback control complex dynamical networks with time-varying delays, utilizing the continuation theorem of coincidence degree theory, a combinatorial identity about Kirchhoff's matrix tree theorem in graph theory, and Lyapunov method. The effectiveness and practicability of the results are demonstrated through a numerical example and its simulation.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Astronomy & Astrophysics
Fabrizio Di Giovanni, Davide Guerra, Simone Albanesi, Miquel Miravet-Tenes, Dimitra Tseneklidou
Summary: The study constructs spherically symmetric static solutions describing gravitationally bound composites of fermions and axions, known as fermion-axion stars. Through numerical simulations, it is found that there may exist multiple stable branches and multiple islands of stability in the existence domain.
Article
Mathematics, Applied
Mei Xu, Bo Du
Summary: This paper studies a second-order nonlinear equation with mixed delays. It establishes some sufficient conditions for the existence and exponential stability of almost periodic solutions. The results of this paper extend the existing ones.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Mathematics, Interdisciplinary Applications
N. Boonsatit, R. Sugumar, D. Ajay, G. Rajchakit, C. P. Lim, P. Hammachukiattikul, M. Usha, P. Agarwal
Summary: This article examines the mixed Script capital H-infinity and passivity synchronization of Markovian jumping neutral-type complex dynamical network (MJNTCDN) models with randomly occurring coupling delays and actuator faults. Novel Lyapunov-Krasovskii functional (LKF) is constructed to verify the stability of the error model and performance level, using Jensen's inequality and a new integral inequality. Sufficient conditions for the synchronization error system (SES) are given in terms of linear matrix inequalities (LMIs), with numerical illustrations provided to exhibit the usefulness of the obtained results.
Article
Engineering, Multidisciplinary
Kevin Linka, Amelie Schafer, Xuhui Meng, Zongren Zou, George Em Karniadakis, Ellen Kuhl
Summary: Understanding real-world dynamical phenomena is challenging, and machine learning has become the go-to technology for analyzing and making decisions based on these phenomena. However, traditional neural networks often ignore the fundamental laws of physics and fail to make accurate predictions. In this study, the combination of neural networks, physics informed modeling, and Bayesian inference is used to integrate data, physics, and uncertainties, improving the predictive potential of neural network models.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Wanqin Wu, Li Yang, Yaping Ren
Summary: This paper investigates the periodic solutions for a class of stochastic neural networks with time-varying delays, establishing sufficient conditions on the existence and exponential stability of periodic solution using fixed points principle and Gronwall-Bellman inequality. The theoretical results are validated through a numerical example, showing applicability to the corresponding deterministic systems.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2021)
Review
Computer Science, Artificial Intelligence
Adnene Arbi, Yingxin Guo, Jinde Cao
Summary: This study introduces the concept of Stepanov-like weighted pseudo almost automorphic on time-space scales and a novel model of high-order BAM neural networks with mixed delays. By constructing Lyapunov-Krasovskii functional and applying Banach's fixed-point theorem, new sufficient conditions are obtained for convergence to the Stepanov-like WPAA solution on time-space scales for labeled neural networks. Theoretical outcomes are validated through numerical examples.
NEURAL COMPUTING & APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Zulqurnain Sabir, Sahar Saoud, Muhammad Asif Zahoor Raja, Hafiz Abdul Wahab, Adnene Arbi
MATHEMATICS AND COMPUTERS IN SIMULATION
(2020)
Article
Mathematics, Interdisciplinary Applications
Guo Yingxin, Shuzhi Sam Ge, Adnene Arbi
Summary: This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks. Through the weighted energy method, comparison principle, and the first integral mean value theorem, it is proven that solutions converge time-exponentially to the corresponding traveling waves under certain conditions.
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
(2022)
Article
Mathematics, Interdisciplinary Applications
Adnene Arbi
Summary: This study investigates the exponential stability of monotone traveling wave solutions for a class of nonlinear delayed dynamical neural networks with leakage term and distributed delays. The new outcomes are obtained by applying Ikeharas theorem, the weighted energy method, Taylor formula, comparison principle, and the first integral mean value theorem. Additionally, the leakage term is considered for the first time in this work for the dynamical model of cellular neural networks.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Electrical & Electronic
Adnene Arbi, Najeh Tahri, Chaker Jammazi, Chuangxia Huang, Jinde Cao
Summary: This paper investigates a class of inertial neural networks with leakages and varying delays on timescales, focusing on the existence, uniqueness, and exponential stability of almost anti-periodic solutions. By constructing Lyapunov functions and applying classical inequalities, sufficient conditions are established to guarantee the main results. A numerical example is provided for illustration.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Adnene Arbi, Najeh Tahri
Summary: This paper investigates a class of inertial neural networks with time delays. By employing the approach of differential inequality techniques coupled with Lyapunov function method, the exponential stability of almost anti-periodic solutions for the dynamical system described by the model is demonstrated. Two numerical examples are provided to illustrate the feasibility of the theoretical outcomes.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematical & Computational Biology
Adnene Arbi
Summary: This research focuses on the control problem for the Fornasnisi-Marchesini model, which takes into account random packet loss and quantization errors in the network environment. A new modeling method is proposed to achieve better stabilization effects. Random packet dropouts, time delays, and quantization are simultaneously considered in the feedback control problem. A logarithmic quantizer is used for quantizing signal measurements, which are handled by a sector bound method. The random packet dropouts are modeled as a Bernoulli process. The use of the Schur complement helps in lightening the assumptions and both state feedback and observer-based output feedback controllers are designed to ensure asymptotic stability of the closed-loop systems.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2022)
Article
Mathematics, Applied
Adnene Arbi, Najeh Tahri
Summary: This work investigates the problem of pseudo Weyl almost periodic solution in quaternion-valued shunting inhibitory model of type cellular neural networks with time-varying delays on time space scales. The concept of pseudo Weyl almost periodicity on time scales is introduced, and sufficient conditions for the existence and stability are given using fixed point theorem, the theory of time scales, Holder's inequality, and Gronwall's inequality. A numerical application is also presented to demonstrate the feasibility of the outcomes.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics
Zulqurnain Sabir, Atef F. Hashem, Adnene Arbi, Mohamed Abdelkawy Abdelhalim
Summary: This study provides numerical solutions for the mathematical model based on the fractional-order Layla and Majnun model (MFLMM). It utilizes a soft computing stochastic-based Bayesian regularization neural network approach (BRNNA) to investigate the numerical achievements of the MFLMM. The BRNNA's accuracy is observed by comparing results, and the reducible performance of the absolute error improves the precision of the computational BRNNA. Twenty neurons were chosen, with training data statistics of 74% and 13% for authorization and testing. The consistency of the designed BRNNA is demonstrated using correlation/regression, error histograms, and the transition of state values to solve the MFLMM.
Article
Mathematics
Zulqurnain Sabir, Adnene Arbi, Atef F. Hashem, Mohamed A. Abdelkawy
Summary: In this study, a design of Morlet wavelet neural networks (MWNNs) is presented, which applies the global approximation capability of a genetic algorithm (GA) and local quick interior-point algorithm scheme (IPAS) to solve the prediction differential model (PDM). Several numerical examples and statistical observations are conducted to verify the authenticity and reliability of MWNN-GAIPAS for solving PDM.
Article
Mathematics, Applied
Adnene Arbi
Summary: In this study, a new robust predictive control technique for uncertain fractional-order descriptor systems is investigated. The existence of a robust predictive controller is guaranteed by minimizing the worst-case optimization problem using the properties of fractional calculus and an appropriate Lyapunov function. The feasibility of the proposed optimization problem at the initial time ensures the admissibility of the fractional-order descriptor closed-loop system.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2023)
Article
Mathematics, Applied
Adene Arbi, Jinde Cao, Mohssine Es-saiydy, Mohammed Zarhouni, Mohamed Zitane
Summary: In this study, we investigate a model of delayed cellular neural networks and derive conditions for the existence and stability of pseudo almost automorphic solutions. The effectiveness of our theoretical results is confirmed through numerical examples and simulations.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2022)
Article
Mathematics, Applied
Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Adnene Arbi, Gilder Cieza Altamirano, Jinde Cao
Summary: This study proposed a novel Neuro swarm computing standards, GNN-PSO-SQPS, to solve a class of second order Lane-Emden singular nonlinear model. By combining Gudermannian neural networks, particle swarm optimization, sequential quadratic programming, and differential operators, the method showed correctness, effectiveness, and competitiveness in solving SO-LES-NM problems. The performance of GNN-PSO-SQPS was tested using statistical operators to ensure constancy, convergence, and precision.
Article
Thermodynamics
Tanveer Sajid, Zulqurnain Sabir, Sumbul Tanveer, Adnene Arbi, Gilder Cieza Altamirano
Summary: Modeling and computations were used to investigate the impact of various factors on Prandtl fluid past a stretching sheet. It was found that an increase in temperature convection parameter leads to an uplift in the temperature profile, and an increase in the chemical reaction coefficient escalates the mass fraction field.
