Article
Mathematics, Interdisciplinary Applications
Binbin Gan, Hao Chen, Biao Xu, Wei Kang
Summary: By constructing an appropriate Lyapunov functional, this paper obtains a novel delay-independent stability criterion for neutral-type Cohen-Grossberg neural networks with multiple time delays. The proposed method reduces computational complexity and conservatism compared to previous literature.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics
Jun Guo, Yanchao Shi, Weihua Luo, Yanzhao Cheng, Shengye Wang, Antonio Lopes
Summary: This paper investigates the adaptive synchronization problem of quaternion-valued Cohen-Grossberg neural networks (QVCGNNs), both with and without known parameters. By constructing an appropriate Lyapunov function and utilizing parameter identification theory and decomposition methods, two effective adaptive feedback schemes are proposed to ensure global synchronization of CGQVNNs. The control gain of these schemes can be obtained using the Matlab LMI toolbox. The theoretical results presented in this work contribute to the literature on exploring the adaptive synchronization problem of quaternion-valued neural networks (QVNNs). Lastly, the reliability of the proposed theoretical schemes is demonstrated through two interesting numerical examples.
Article
Computer Science, Artificial Intelligence
Xiao-Zhen Liu, Kai-Ning Wu, Xiaohua Ding, Weihai Zhang
Summary: This study focuses on the boundary stabilization of stochastic delayed Cohen-Grossberg neural networks with diffusion terms by using boundary control for mean-square exponential stabilization. The effects of diffusion matrix, coupling strength, and time delays on exponentially stability are analyzed, and Poincare's inequality and Schur's complement lemma are used to address the difficulties in system analysis. Additionally, an application of the theoretical result is presented for mean-square exponential synchronization of stochastic delayed Hopfield neural networks under boundary control.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Ozlem Faydasicok, Sabri Arik
Summary: This research article aims to conduct a new Lyapunov stability analysis of a special model of Cohen-Grossberg neural networks with multiple delay terms. The obtained stability results are independent of the time delay terms and are characterized by the interconnection parameters. A numerical example demonstrates the advantages and novelties of these global stability results compared to previously reported conditions.
Article
Mathematics, Applied
Zhongjie Zhang, Tingting Yu, Xian Zhang
Summary: This paper aims to establish global exponential stability criteria for multiple time-varying delay Cohen-Grossberg neural networks. By constructing novel Lyapunov-Krasovskii functionals, two algebraic criteria guaranteeing global exponential stability are given. Numerical examples are used to validate the effectiveness of the obtained criteria.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics
Molan Li, Da Li, Junxing Zhang, Xuanlu Xiang, Di Zhao
Summary: By discussing the dynamical properties of optimal cue integration with time-varying delay, we find that it is asymptotically stable and leads to a unique insect home direction. These results provide a theoretical basis for further research on insect homing behaviors and the establishment of autonomous robots that mimic insect navigation mechanisms in the future.
Article
Mathematics, Applied
M. Manikandan, K. Ratnavelu, P. Balasubramaniam, S. H. Ong
Summary: This paper investigates the synchronization problem of BAM CGFCNNs with discrete time-varying and unbounded distributed delays, and obtains sufficient conditions using Lyapunov-Krasovskii (LK) functional and Linear matrix inequality (LMI) approach to guarantee the synchronization of the system under parametric uncertainty. Numerical examples with simulations are provided to demonstrate the effectiveness of the derived results in ensuring global asymptotic stability of the error dynamics.
IRANIAN JOURNAL OF FUZZY SYSTEMS
(2021)
Article
Engineering, Multidisciplinary
Danning Xu, Wei Liu
Summary: This paper focuses on the stochastic asymptotic stability of stochastic inertial Cohen-Grossberg neural networks with time-varying delay. Firstly, the second-order differential equation is transformed into a first-order differential equation using appropriate variable substitution. Secondly, the existence of equilibrium point is derived using homeomorphic mapping, the finite increment formula of Lagrange mean value theorem, and linear matrix inequality. The conditions for the stochastic asymptotic stability of the system's equilibrium point are obtained by defining the appropriate operator, constructing a positive Lyapunov function, and positive-definite matrix. Lastly, a numerical example is provided to illustrate the accuracy of these theorems.
JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING
(2023)
Article
Mathematics, Applied
Saravanan Shanmugam, R. Vadivel, Mohamed Rhaima, Hamza Ghoudi
Summary: This research investigates the issue of extended dissipative analysis for neural networks with additive time-varying delays. By constructing the augmented Lyapunov-Krasovskii functional and utilizing improved integral inequalities, such as auxiliary function-based integral inequalities, less conservative sufficient conditions are obtained to ensure the asymptotic stability and extended dissipativity of the neural networks. The study aims to solve the H_∞, L_2 - L_∞, passivity, and (Q, S, R)-γ-dissipativity performance problems in a unified framework based on the concept of extended dissipativity. The solvability condition of the designed neural networks with additive time-varying delays is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach are demonstrated through four numerical examples.
Article
Mathematics, Applied
Zerong Ren, Junkang Tian
Summary: This paper researches the problem of stability analysis for distributed time-delay systems. A newly augmented Lyapunov-Krasovskii functional (LKF) is introduced via a generalized delay partitioning approach, and a less conservative stability criterion is derived by introducing a novel Jensen inequality. The stability condition is given in terms of linear matrix inequality.
Article
Automation & Control Systems
Hongjun Qiu, Fanchao Kong
Summary: This paper investigates the global exponential stability of a class of inertial Cohen-Grossberg neural networks with parameter uncertainties and time-varying delays. By constructing a modified delay-dependent Lyapunov-Krasovskii functional, simple algebraic inequalities are given to ensure the stability of the neural network model. The proposed model and results are more general and rigorous compared to existing methods.
INTERNATIONAL JOURNAL OF CONTROL
(2022)
Article
Computer Science, Information Systems
Li Wan, Qinghua Zhou
Summary: This paper addresses the exponential stability of a more general class of neutral-type Cohen-Grossberg neural networks, providing sufficient conditions to ensure the existence, uniqueness, and stability of the equilibrium point of the neural system. The conditions are easy to verify and guarantee global asymptotic stability, with two remarks indicating that they are less conservative than previous results. Two instructive examples are also given to demonstrate the effectiveness of the theoretical results and compare the stability conditions with previous findings.
Article
Computer Science, Information Systems
Hebing Zhang
Summary: This study analyzes the stability of stochastic fuzzy Cohen-Grossberg neural networks (CGNNs) with delayed pth moment exponential stability and almost sure exponential stability. The method used integrates integral inequality, differential inequality, stochastic analysis theory, and Itô's formula. The research provides sufficient conditions for system stability without the need for complex Lyapunov functions. It also confirms the positive effects of fuzzy and stochastic terms on system stability.
Article
Mathematics
Zhengqi Ma, Shoucheng Yuan, Kexin Meng, Shuli Mei
Summary: This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov-Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.
Article
Mathematics, Applied
Qian Li, Liqun Zhou
Summary: In this article, the global asymptotic synchronization (GAS) of inertial memristive Cohen-Grossberg neural networks (IMCGNNs) with proportional delays (PDs) as drive-response systems is studied. The systems are converted to first-order differential systems using differential inclusion theory (DIT) and variable transformation. Feedback and adaptive controllers are designed, which are easy to implement in hardware. Two GAS criteria, expressed as algebraic inequalities, are obtained by constructing Lyapunov functionals and using mean value inequality analysis. Numerical examples with simulations are provided to support the obtained results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
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)
