Article
Computer Science, Artificial Intelligence
Fanghai Zhang, Zhigang Zeng
Summary: This article investigates the multistability and stabilization of fractional-order competitive neural networks with unbounded time-varying delays, deriving conditions for coexistence of equilibrium points and multiple mu-stability through analytical methods. The results enrich and improve previous findings in the field, and are demonstrated to be effective through numerical examples.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Song Zhu, Jiahui Zhang, Xiaoyang Liu, Mouquan Shen, Shiping Wen, Chaoxu Mu
Summary: This article analyzes the multistability and robustness of competitive neural networks with time-varying delays. Sufficient conditions are proposed based on the geometry of activation functions to determine the existence of equilibrium points and their stability. The conclusions proposed in this article are easy to verify and enrich the existing theories.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Fanghai Zhang, Zhigang Zeng
Summary: This article discusses the multistability and attraction of fractional-order neural networks with unbounded time-varying delays. Multiple sufficient conditions are provided for the coexistence of equilibrium points with concave-convex activation functions. The criteria for Mittag-Leffler stability can be simplified to M-matrix and the extension of attraction basin is shown to be independent of the magnitude of delays. Three numerical examples are given to demonstrate the validity of the theoretical results.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
Article
Mathematics, Applied
Yan Zhang, Yuanhua Qiao, Lijuan Duan, Jun Miao
Summary: This paper addresses the problem of multistability in competitive neural networks with nonlinear, non-monotonic piecewise activation functions and time-varying delays. Sufficient conditions are proposed for the existence and stability of equilibrium points, and the quantitative relationship between the equilibrium points and the zero roots of bounding functions is given. Additionally, the attraction basins of exponentially stable equilibrium points are obtained.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Zhenyuan Guo, Shiqin Ou, Jun Wang
Summary: This article discusses the multistability of switched neural networks with Gaussian activation functions under state-dependent switching, showing how the equilibrium points can be characterized using geometrical properties and local linearization. By deriving sufficient conditions, it is demonstrated that the networks can have up to 7(n) equilibria, with up to 4(n) of them being locally stable when p(1) = n. Proper selection of parameters can lead to a desired number of stable equilibria. Two numerical examples are provided to support the theoretical results.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Zhongwen Wu, Xiaobing Nie, Boqiang Cao
Summary: This paper investigates the coexistence and local stability of multiple equilibrium points for a class of competitive neural networks with sigmoidal activation functions and time-varying delays, in which both fractional-order derivative and state-dependent switching are involved. Novel criteria are established to ensure the existence of equilibrium points and their local stability. The investigation reveals that competitive neural networks with switching can have greater storage capacity than those without switching. The results generalize and improve existing works by including both fractional-order and integer-order switched Hopfield neural networks as special cases. Numerical examples are presented to validate the theoretical analysis.
Article
Computer Science, Artificial Intelligence
Peng Wan, Dihua Sun, Min Zhao, Shuai Huang
Summary: This article investigates the multistability of almost-periodic solutions of Takagi-Sugeno fuzzy neural networks with nonmonotonic discontinuous activation functions and time-varying delays. By analyzing the geometric properties of nonmonotonic activation functions, it is demonstrated that the addressed networks have a locally exponentially stable almost-periodic solution under certain conditions. The study also estimates the attraction basins, showing that they can be larger than the original hyperrectangular regions.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yang Liu, Zhen Wang, Xia Huang
Summary: This study investigates the multistability of SSHNNs with the Gaussian-wavelet-type activation function and finds that it has more locally stable equilibria, increasing storage capacity and advantages in associative memory applications.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Siyi Yu, Hua Li, Xiaofeng Chen, Dongyuan Lin
Summary: This paper proposes a design for a system with high storage capacity for associative memory and pattern recognition. A quaternion-valued neural network (QVNN) model with multiple equilibrium points is introduced, using the cosine function as the activation function of QVNN. Sufficient conditions are then derived for QVNN to have unique, finite, and countable infinite equilibrium points based on the Brouwer fixed point theorem and the geometric properties of the activation function. The paper also establishes sufficient conditions for the exponential stability of equilibrium points and provides the attraction basins of stable equilibrium points. Two numerical examples are presented to validate the proposed theoretical results.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Artificial Intelligence
Fanghai Zhang, Tingwen Huang, Qiujie Wu, Zhigang Zeng
Summary: This paper investigates the multistability of fractional-order competitive neural networks with time-varying delays. The equilibrium points of the networks are given by division of state space, and several sufficient conditions and criteria are proposed to ascertain the multiple stability of the networks. Additionally, the attraction basins of the stable equilibrium points are estimated, showing that they can be larger than the divided subsets.
Article
Engineering, Electrical & Electronic
Ailong Wu, Yue Chen, Song Zhu, Shiping Wen
Summary: This article focuses on the positivity and stability of Cohen-Grossberg-type time-delay memristor neural networks. By extending the existence and uniqueness theorem to unbounded delays, utilizing Lyapunov method and memristor nonlinearity, sufficient and necessary conditions for positivity and stability under unbounded delays are obtained, contributing to understanding the convergence performance of memristor electrical systems.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2021)
Article
Computer Science, Artificial Intelligence
Xiaobing Nie, Pingping Liu, Jinling Liang, Jinde Cao
Summary: This paper investigates the multistability issue of fractional-order Hopfield neural networks with Gaussian activation function and multiple time delays. The study presents criteria for ensuring the existence of 3(n) equilibria, and shows that 2(n) of them are locally asymptotically stable. The results extend existing works on multistability in integer-order and fractional-order neural networks.
Article
Computer Science, Artificial Intelligence
Liguang Wan, Zhenxing Liu
Summary: This paper formulates multiple exponential stability and instability for a class of state-dependent switched neural networks with time-varying delays. It divides the index set into different categories based on the switching threshold. By obtaining the invariant intervals in these categories, the state space is partitioned into multiple regions. By applying reduction to absurdity, function continuity and monotonicity, as well as Lyapunov method, the paper establishes sufficient conditions for the existence of unique equilibrium points in each region and their stability properties.
Article
Computer Science, Artificial Intelligence
Weihao Du, Jianglian Xiang, Manchun Tan
Summary: This article investigates the coexistence and dynamical behaviors of multiple equilibrium points for quaternion-valued neural networks with discontinuous and nonmonotonic piecewise nonlinear activation functions. By utilizing mathematical theorems and matrix properties, sufficient conditions are derived to ensure the existence of multiple stable equilibrium points in the network. Numerical simulations are provided to validate the theoretical analysis.
NEURAL PROCESSING LETTERS
(2023)
Article
Computer Science, Artificial Intelligence
Yuanchu Shen, Song Zhu, Xiaoyang Liu, Shiping Wen
Summary: This paper discusses the multistability analysis and associative memory of neural networks with Morita-like activation functions, proposing a larger memory capacity. The NNs with n-neurons have equilibrium points and locally exponentially stable points, with the parameter m depending on the Morita-like activation functions. The application of these NNs to associative memories results in significantly increased memory capacity compared to previous works.
Article
Computer Science, Artificial Intelligence
Tengda Wei, Xiaodi Li, Jinde Cao
Summary: This article focuses on stability analysis of delayed reaction-diffusion neural-network models with hybrid impulses. The Krasovskii-type theorems are established for sufficient conditions of exponential stability, allowing the existence of impulsive perturbation in some nodes and time. The effectiveness of theoretical results is verified by numerical examples with a successful application to image encryption.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics, Applied
Hongjie Li, Jinde Cao
Summary: This paper investigates the event-triggered group consensus problem for multi-agent systems with input saturation under both fixed topology and Markovian switching topologies. The agent dynamics are described by a one-sided Lipschitz nonlinear function, which covers a wide range of nonlinear systems. A novel distributed dynamic event-triggered communication scheme based on local stochastic sampling information is proposed. The paper also derives local group consensus criteria for the mean square condition under fixed topology and Markovian switching topologies using a stochastic sampled-data dependent error system obtained through model transformation. An optimization algorithm is introduced for estimating the region of initial conditions, and numerical examples are provided to illustrate the effectiveness of the theoretical results. (c) 2023 Elsevier B.V. All rights reserved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Automation & Control Systems
Lifei Xie, Jun Cheng, Jinde Cao, Mengjie Hu
Summary: This paper focuses on the control design problem for wind turbine generator systems (WTGSs) using a proportional-integral observer. A semi-Markov jump process is used to describe the operation points of WTGSs between different subareas considering variable wind speed. An adaptive-memory event-triggered protocol (AMETP) is constructed for efficient transmission frequency modulation, resulting in improved dynamic performance. Sufficient criteria for the stochastic stability of the closed-loop systems are formulated based on parameter-dependent Lyapunov stability theory. The feasibility of the approach is demonstrated through a numerical example.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Artificial Intelligence
Xinbin Chen, Hai Zhang, Renyu Ye, Qinyun Lu, Jinde Cao
Summary: This article analyzes the issues of quasi-projective synchronization (QPS) for delayed Caputo-type BAM neural networks in the complex field. The non-decomposition method is adopted to facilitate calculation and realize QPS. A novel lemma in the form of algebraic inequality is established based on the Laplace transform to deal with the delay term. Criteria for QPS are obtained using the proposed lemma, inequality techniques, and Lyapunov method, along with the design of different controllers. The rationality of the criteria is tested through simulations.
NEURAL PROCESSING LETTERS
(2023)
Article
Engineering, Mechanical
Chengdai Huang, Jie Gao, Shansong Mo, Jinde Cao
Summary: This paper deals with the bifurcation problem of a two-delayed fractional-order neural network (FONN) with three neurons. The bifurcation progresses are captured by using the self-connecting delay and communication delay as bifurcation parameters. The stability and bifurcation conditions of the FONN are discussed and verified through numerical simulations.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Weiying Shang, Weiwei Zhang, Hai Zhang, Hongmei Zhang, Jinde Cao, Fawaz E. Alsaadi
Summary: This paper discusses the finite-time lag projective synchronization (FTLPS) of delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, and solves it using a non-decomposition method. A new delayed FOQVNNs model with uncertain parameters is designed, and two types of feedback controller and adaptive controller without sign functions are designed in the quaternion domain. The non-decomposition method is applied, combined with some quaternion inequality techniques, to accurately estimate the settling time of FTLPS. The obtained theoretical results are verified by a numerical simulation example.
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2023)
Article
Mathematics, Applied
Haomin Bai, Wenying Xu, Shaofu Yang, Jinde Cao
Summary: This paper investigates the problem of distributed generalized Nash equilibrium (GNE) tracking in a dynamic environment. It proposes a distributed inertial online game (D-IOG) algorithm to track Nash equilibrium (NE) in the absence of coupled constraints. Furthermore, it introduces a modified D-IOG algorithm based on primal-dual and mirror descent methods to handle time-varying coupled constraints. Simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.
Article
Construction & Building Technology
Yingcheng Luan, Weiguang Zhang, Tao Ma, Jinde Cao, Xinli Shi, Zheng Tong
Summary: Overlaying is a popular method to improve pavement quality. This study evaluates existing pavement conditions and crack patterns before and after asphalt overlaying. The findings indicate the presence of thermal and reflective cracks, with identified factors affecting the different crack patterns. Finite Element Method analysis shows that crack propagation and resistance are influenced by the modulus of the existing layer and the aging effect of the overlay. A proposed overlaying strategy with multi-layer overlays and geogrid is found effective in reducing reflective cracks through simulative modeling.
CONSTRUCTION AND BUILDING MATERIALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Jinde Cao, Ashish
Summary: Chaos is a nonlinear phenomenon that is present in nature and various scientific fields. This article focuses on the study of a discrete two-parameter map, which is a composition of Euler's numerical map and the logistic map. The nature of fixed and periodic states, as well as the onset of chaos and its dynamical properties, are examined in detail through experimental and numerical simulations, and various scaling methods are used to analyze the appearance of chaos.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Physics, Multidisciplinary
Yuwei Yang, Zhuoxuan Li, Jun Chen, Zhiyuan Liu, Jinde Cao
Summary: This paper proposes an extreme learning machine (ELM) algorithm based on residual correction and Tent chaos sequence (TRELM-DROP) for accurate prediction of traffic flow. The algorithm reduces the impact of randomness in traffic flow through the Tent chaos strategy and residual correction method, and avoids weight optimization using the iterative method. A DROP strategy is introduced to improve the algorithm's ability to predict traffic flow under varying conditions.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Computer Science, Artificial Intelligence
Chen Liu, Lei Liu, Jinde Cao, Mahmoud Abdel-Aty
Summary: This article investigates the intermittent event-triggered optimal leader-following consensus for nonlinear multi-agent systems (MASs) utilizing the actor-critic algorithm. The article proposes a novel distributed intermittent event-triggered control strategy and establishes a new piecewise differential inequality to guarantee the leader-following consensus of MASs. The article also designs an intermittent event-triggered optimal control strategy and proves the optimality of MASs and the stability of the closed-loop system. Additionally, an intermittent event-triggered approximate optimal control strategy is implemented using an actor-critic network, and the occurrence of Zeno behavior is excluded. Simulation examples further verify the effectiveness of the proposed scheme.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematical & Computational Biology
Duoduo Zhao, Fang Gao, Jinde Cao, Xiaoxin Li, Xiaoqin Ma
Summary: This paper focuses on achieving leader-follower mean square consensus in semi-Markov jump multi-agent systems. To reduce communication costs and control updates effectively, an event-triggered protocol based on stochastic sampling is proposed. The stochastic sampling interval randomly switches between finite given values, while the event-triggered function depends on the stochastic sampled data from neighboring agents. Sufficient conditions to ensure mean square consensus are presented using the event-triggered strategy, and a numerical example is provided to demonstrate the effectiveness of the theoretical results.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Computer Science, Artificial Intelligence
Xue Wang, Zheng Guan, Wenhua Qian, Jinde Cao, Chengchao Wang, Runzhuo Ma
Summary: This paper proposes a semisupervised transfer learning-based method called STFuse for infrared and visible image fusion (IVIF). By borrowing supervised knowledge from multifocus image fusion (MFIF) task and using a guidance loss, the method effectively utilizes cross-task knowledge to alleviate the limitation of the lack of ground truth. The design of a cross-feature enhancement module further enhances visual quality, statistical metrics, and docking performance with high-level vision tasks.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics, Applied
Wenjie Li, Yajuan Guan, Jinde Cao, Fei Xu
Summary: This article establishes the global stability of the disease-free equilibrium in a degenerate diffusion system involving environmental transmission and spatial heterogeneity. It provides important insights into the transmission dynamics of avian influenza virus among avian, poultry, and human populations.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Computer Science, Artificial Intelligence
Hanjie Liu, Jinde Cao, Wei Huang, Xinli Shi, Xingye Zhou, Zhuoxuan Li
Summary: A data-driven multidimensional framework is proposed to evaluate pavement condition by utilizing multilayer network representation learning. The method can capture the nonlinear interactions among performance attributes and provide a more in-depth understanding of pavement service condition. Experimental results demonstrate the effectiveness of this method in multi-attribute evaluation.
EXPERT SYSTEMS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
