Article
Computer Science, Artificial Intelligence
Ming Jin, Yu Zheng, Yuan-Fang Li, Siheng Chen, Bin Yang, Shirui Pan
Summary: This paper proposes a continuous model, MTGODE, to forecast multivariate time series by overcoming the limitations of discrete neural architectures, high complexity, and reliance on graph priors. MTGODE utilizes dynamic graph neural ordinary differential equations to unify spatial and temporal message passing, resulting in superior forecasting performance on benchmark datasets.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
(2023)
Article
Computer Science, Information Systems
Yingji Li, Yue Wu, Mingchen Sun, Bo Yang, Ying Wang
Summary: This study proposes a Transformer-based continuous dynamic network representation learning model called T-TGNN, which aggregates global information in continuous dynamic networks. By modeling the temporal changes in networks using ordinary neural differential equations and utilizing Transformer mechanisms to aggregate temporal and structural information, this model can better capture the evolution of dynamic networks.
INFORMATION SCIENCES
(2023)
Article
Mathematics, Applied
Jaqueline G. Mesquita, Aldo Pereira, Rodrigo Ponce
Summary: This paper introduces the definition of cosine and sine functions on time scales and investigates their properties and relationship with their infinitesimal generator. It also applies this theory to study abstract Cauchy problems on time scales in Banach spaces.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Zareen A. Khan, Kadir Kaynak
Summary: Based on existing Gronwall inequalities, this research introduces new nonlinear dynamic inequalities on time scales related to an independent variable. These inequalities can serve as powerful tools for determining the characteristics of various dynamic equations on time scales and open up new possibilities for studying the structure of time scale schemes.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics
A. Hassan, Ismoil Odinaev, Taher S. Hassan
Summary: The objective of this article is to examine the oscillatory behavior of a class of quasilinear second-order dynamic equations on time scales. Our focus is on the noncanonical case, and we transform it into a corresponding canonical equation to develop new and more efficient oscillation criteria. Applying these results to specific cases, we demonstrate their significance and usefulness.
JOURNAL OF MATHEMATICS
(2023)
Article
Computer Science, Artificial Intelligence
Xiangxiang Wang, Yongbin Yu, Jingye Cai, Shouming Zhong, Nijing Yang, Kaibo Shi, Pinaki Mazumder, Nyima Tashi
Summary: This article addresses the problem of dynamic pinning synchronization in fuzzy-dependent-switched coupled memristive neural networks with mismatched dimensions on time scales. The article introduces a novel CMNNs model design to enhance reliability and generalization ability. The Fds rules and dynamic pinning control method are adopted to improve information exchange and utilization of communication bandwidth. The article also proposes a solution for information exchange and data sharing between systems of different dimensions. The proposed conditions for modified function projective synchronization are derived via the DPC method on time scales. The effectiveness of the main results is demonstrated through numerical examples.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2022)
Article
Automation & Control Systems
Zhijun Zhang, Lihang Ye, Lunan Zheng, Yamei Luo
Summary: This article presents a novel approach of using an integral dynamic learning network (IDLN) to solve a general time-varying Lyapunov matrix equation (TVLME). A cost function is defined by designing a variable unbounded vector/matrix-type error function, with the goal of approximating the cost function to zero. An integral neural dynamic equation with an odd activation function is designed to guarantee convergence to zero. A novel IDLN with a recurrent topological structure is utilized to find the time-varying theoretical solution. The proposed IDLN shows strong robustness to bounded noise with unknown amplitude, making it suitable for parallel computing and achieving global convergence.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Applied
Yongkun Li, Shiping Shen
Summary: This paper introduces the concept of compact almost automorphic functions on time scales and studies their properties, including characterization, composition theorems, and completeness. It also proves the existence and global exponential stability of a class of Clifford-valued recurrent neural networks with time-varying delays, demonstrating the feasibility of the results through an example.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2021)
Article
Mathematics
Ya-Ru Zhu, Zhong-Xuan Mao, Jing-Feng Tian, Ya-Gang Zhang, Xin-Ni Lin
Summary: In this paper, we investigate two universal higher order dynamic equations with several delay functions. By utilizing the fixed point theorem, we establish two oscillatory criteria for the first equation and a sufficient and necessary condition for the second equation to have a nonoscillatory solution.
Article
Computer Science, Artificial Intelligence
Wu Yang, Yan-Wu Wang, Irinel-Constantin Morarescu, Xiao-Kang Liu, Yuehua Huang
Summary: This paper investigates fixed-time synchronization of competitive neural networks with multiple time scales, proposing a synchronizing controller that is independent of the ratio between fast and slow time scales, showing high convergence speed and bounded settling time in closed-loop dynamics. Numerical simulations support the effectiveness of the results.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Review
Physics, Multidisciplinary
Chao Wang, Ravi P. Agarwal
Summary: Time scale calculus serves as an effective tool to unify discrete and continuous analysis, and has unique features that differentiate it from difference and differential equations in describing complex dynamical behavior. This review article surveys abstract analysis and applied dynamic equations on hybrid time scales, highlighting recent main results and discussing future research directions in this field. The presented results can be extended and generalized for studies in pure mathematical analysis and various real-world applications like mathematical physics, biological dynamical models, and neural networks.
Article
Mathematics, Applied
Martin Bohner, Tom Cuchta, Sabrina Streipert
Summary: In this paper, we investigate the properties of delay differential and difference equations with constant coefficients based on their one-periodic nature. We propose a definition of periodicity for arbitrary isolated time scales and apply it to linear and nonlinear delay dynamic equations. By utilizing a derived identity of higher order delta derivatives and delay terms, we simplify the considered equations and express them as a linear autonomous dynamic system with constant matrix.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Multidisciplinary Sciences
Lea-Maria Schmitt, Julia Erb, Sarah Tune, Anna U. Rysop, Gesa Hartwigsen, Jonas Obleser
Summary: The brain incorporates the temporal unfolding of context in a hierarchical manner by sparsely updating contextual representations at event boundaries. Training artificial neural networks and using functional magnetic resonance imaging reveal an event-based surprisal hierarchy evolving along a temporoparietal pathway. Surprisal influences connectivity between neighboring time scales and temporoparietal activity, demonstrating an efficient and contextually diverse network architecture for predictions.
Article
Mathematics, Applied
Said R. Grace, G. N. Chhatria, Syed Abbas
Summary: In this paper, some new oscillation results are presented for the second order nonlinear delay dynamic equation of the form (r(0)(z(Delta)(0))(alpha))(Delta) + q(0)z(nu)(omega(0)) = 0 where 0 is an element of(sic)(0) = [0(0) ,infinity) boolean AND (sic). New monotonic properties of the nonoscillatory solutions are derived and used to linearize the equation. The presented results are verified by some illustrative examples.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Zhongyang Ming, Huaguang Zhang, Yuling Liang, Hanguang Su
Summary: In this paper, a single network adaptive dynamic programming (ADP) control method is proposed for the non-zero sum (NZS) differential game problem of the autonomous nonlinear system. The Osgood condition is introduced to ensure the existence and uniqueness of the solution of the dynamic nonlinear systems and to weaken the limited conditions of nonlinear dynamic functions. The proposed method achieves real-time approximations of the optimal value and the non-zero sum Nash-equilibrium, while ensuring the uniform ultimate epsilon-boundedness of the closed-loop system. The effectiveness of the method is verified through a simulation example.
APPLIED MATHEMATICS AND COMPUTATION
(2022)