Article
Mathematics, Applied
Ankit Kumar, Subir Das, Vijay K. Yadav, Rajeev, Jinde Cao, Chuangxia Huang
Summary: This article investigates finite-time and fixed-time synchronizations of fuzzy cellular neural networks with interaction and proportional delay terms. Synchronization is achieved using p-norm based on defined inequalities, and Lyapunov stability theory and controllers are utilized to achieve FFTS with an upper bound on settling time. The theoretical results are shown to be more general compared to fixed time synchronization through numerical examples.
Article
Physics, Multidisciplinary
Fahhad H. Alharbi, Abdelrahman S. Abdelrahman, Abdullah M. Alkathiry, Hussain M. Al-Qahtani
Summary: In this study, the Frimmer-Novotny model for simulating two-level systems by coupled oscillators is extended by incorporating a constant time delay in the coupling. The effects of this delay on system dynamics and two-level modeling are investigated and found to be substantial. The results show that the delay has oscillatory effects on the system dynamics and can govern the energy transfer dynamics and coherence. The delay and the coupling strength both play a critical role in determining the stability of the system.
Article
Automation & Control Systems
Vittorio De Iuliis, Alessandro D'Innocenzo, Alfredo Germani, Costanzo Manes
Summary: This article presents novel results on the stability of linear coupled differential-difference systems with multiple time-varying delays, introducing necessary and sufficient conditions for positivity and delay-independent stability, and demonstrating how these results can be systematically applied to non-positive systems. As a result, new stability results on neutral-type systems, differential systems, and continuous-time difference systems with multiple delays are obtained.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2021)
Review
Mathematics, Applied
Nicolas Torres, Maria J. Caceres, Benoit Perthame, Delphine Salort
Summary: The elapsed time model, a subject widely studied in mathematical neuroscience, focuses on the dynamics of interacting neurons structured by the time since their last discharge. The model presents challenges in highly connected networks with strong nonlinearities, leading to the use of perturbation methods. Different cases of inhibitory, weakly excitatory, and strongly excitatory scenarios are analyzed, showing convergence to stationary states and existence of periodic solutions. Numerical simulations are presented to validate the theoretical results.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Physics, Multidisciplinary
Shidong Zhai, Tao Huang, Guoqiang Luo, Xin Wang, Jun Ma
Summary: This paper investigates the problem of synchronization in coupled nonlinear systems with antagonistic interactions and bounded time delay. By designing a pinning scheme, the network is able to achieve bipartite synchronization. Conditions for bipartite synchronization with non-differentiable and differentiable coupling delays are derived and formulated as linear matrix inequalities. Numerical examples are provided to illustrate the effectiveness of the results.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Mathematics, Applied
Yan Liu, Yutong Lin
Summary: This paper investigates the problem of exponential synchronization of quaternion-valued coupled systems based on event-triggered impulsive control for the first time. The study proves that event-triggered impulsive control can exclude Zeno behavior and provides sufficient conditions for synchronization based on Lyapunov method and graph theory. The effectiveness of the theoretical results is demonstrated through numerical simulations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Hongling Qiu, Jinde Cao, Heng Liu
Summary: This work aims to investigate the positivity, stability, and LW-gain of incommensurate fractional-order coupled differential-difference systems with unbounded time-varying delays. The existence and uniqueness of solutions are proven using the Banach's fixed point theorem. A criterion for ensuring the positivity and stability is proposed, and auxiliary systems are developed to calculate the LW-gain.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Hui Zhou, Yuting Chen, Dianhui Chu, Wenxue Li
Summary: This paper investigates the stabilization problem of stochastic Levy noise coupled systems with time delays and regime switching diffusions (SLCSTR) using intermittent control with a time delay (ICTD). The paper proposes a novel approach that combines the benefits of aperiodically intermittent control and delay feedback control. The paper also provides stabilization criteria for SLCSTR based on Lyapunov method, graph theory, and inequalities. Furthermore, the paper explores the practical application of the theoretical results in stochastic delayed coupled oscillators with Levy noise and regime switching diffusions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Computer Science, Information Systems
Jingjing Yan, Xiaofan Mao, Yuanqing Xia, Lan Wu
Summary: This paper studies the output feedback stabilization of linear switched systems with quantization and time-delay. By designing a feedback controller based on a state observer, the mismatch between system and controller modes, the difficulty of quantization rules design, and the challenges of state reconstruction are addressed.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Information Systems
Wenyou Liu, Yunjun Bai, Li Jiao, Naijun Zhan
Summary: This paper investigates the safety verification problem of time-delay systems modeled by nonlinear delay differential equations with control inputs and disturbances. The notions of input-to-state safety and input-to-state safe control barrier functionals are developed based on classical control barrier functionals to ensure the safety of such systems. Three examples are provided to illustrate the proposed approach.
SCIENCE CHINA-INFORMATION SCIENCES
(2023)
Article
Optics
Xueting Zhang, Gang Guo, Xintian Liu, Guosi Hu, Kun Wang, Penghua Mu
Summary: In this paper, the dynamic behavior and time-delay concealment properties of mutually coupled nano-lasers in different structures were numerically investigated. The results show that adding feedback in the mutually coupled scheme can improve the quality of chaotic signals, and selecting appropriate parameters can achieve better time-delay concealment.
Article
Automation & Control Systems
Vukan Turkulov, Milan R. Rapaic, Rachid Malti
Summary: This paper presents a novel method for stability analysis of a wide class of linear, time-delay systems. The proposed method is based on frequency domain analysis and application of Rouche's theorem. The method can identify the surrounding region in the parametric space for which the number of unstable poles remains invariant and is applicable to parameters of different types, as illustrated by examples.
Article
Mathematics, Applied
Zhiyuan Li, Xinchi Huang, Yikan Liu
Summary: This article studies the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. By defining the mild solution, fundamental unique existence, limited smoothing property, and long-time asymptotic behavior of the solution are established, which mostly inherit those of a single equation. Due to the coupling effect, we also obtain the uniqueness of an inverse problem in determining all the fractional orders by the single point observation of a single component of the solution.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2023)
Article
Physics, Multidisciplinary
Yiping Luo, Yuejie Yao, Zifeng Cheng, Xing Xiao, Hanyu Liu
Summary: This paper investigates finite-time synchronization in a class of coupled nonlinear reaction-diffusion complex network system using event-triggered control. Several sufficient conditions for achieving synchronization are obtained by combining distributed event-triggered control protocol with Lyapunov stability theorem, Green formula, matrix inequality, and partial differential equation theory. The upper bound of time for achieving synchronization is estimated, and numerical simulation is used to validate the theory.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Automation & Control Systems
Shuqing Gong, Zhenyuan Guo, Shiping Wen, Tingwen Huang
Summary: This article examines the finite-time and fixed-time synchronization of coupled memristive neural networks with time delays. By introducing a proper controller and utilizing the Lyapunov method, the synchronization conditions are obtained. It is leaderless synchronization with estimated settling times.
IEEE TRANSACTIONS ON CYBERNETICS
(2021)
Article
Physics, Multidisciplinary
S. Stalin, R. Ramakrishnan, M. Lakshmanan
Article
Physics, Applied
R. Arun, R. Gopal, V. K. Chandrasekar, M. Lakshmanan
JOURNAL OF APPLIED PHYSICS
(2020)
Editorial Material
Physics, Mathematical
V. K. Chandrasekar, A. K. Tiwari, S. N. Pandey, M. Senthilvelan, M. Lakshmanan
JOURNAL OF MATHEMATICAL PHYSICS
(2020)
Article
Physics, Multidisciplinary
M. Sathish Aravindh, R. Gopal, A. Venkatesan, M. Lakshmanan
PRAMANA-JOURNAL OF PHYSICS
(2020)
Article
Engineering, Mechanical
I Gowthaman, K. Sathiyadevi, V. K. Chandrasekar, D. Senthilkumar
NONLINEAR DYNAMICS
(2020)
Article
Physics, Multidisciplinary
A. K. Shafeeque Ali, M. Lakshmanan
Article
Physics, Multidisciplinary
A. K. Shafeeque Ali, Malik Zaka Ullah, M. Lakshmanan
Article
Mathematics, Interdisciplinary Applications
I Gowthaman, Uday Singh, V. K. Chandrasekar, D. Senthilkumar
Summary: The deterioration or failure of a small fraction of microscopic constituents in a network can lead to loss of its macroscopic activity. The evolution equation of two macroscopic order parameters is deduced from a globally coupled network of oscillators, facilitating classification of stable states. The network's dynamical robustness is examined by introducing limiting factors and self-feedback, alongside heterogeneity.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
A. Sharafali, A. K. Shafeeque Ali, M. Lakshmanan
Summary: In this paper, a liquid core suspended photonic crystal fiber (LCSPCF) is proposed as a potential waveguide structure for nonlinear applications, emphasizing the improved nonlinear properties through liquid infiltration and suspension effect. The study reveals that quintic nonlinearity (QN) enhances modulation instability for cooperating nonlinearities and suppresses it for competing nonlinearities. Additionally, the effect of QN on modulation instability induced supercontinuum generation (SCG) in silica and CS2 liquid core PCF was investigated.
Article
Mathematics, Interdisciplinary Applications
K. Sathiyadevi, D. Premraj, Tanmoy Banerjee, Zhigang Zheng, M. Lakshmanan
Summary: We investigated the aging transition in a globally coupled network of Stuart-Landau oscillators under discrete time-dependent coupling. Our findings reveal that by adjusting the time period and duty cycle of the ON-OFF intervals, the aging region can significantly shrink, leading to the restoration of oscillatory dynamics. The results also indicate that the type of coupling and pulse interval play crucial roles in controlling the aging dynamics, providing a noninvasive approach to restore oscillatory dynamics from an aging state in a coupled oscillator network.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
V. K. Chandrasekar, R. Gladwin Pradeep, R. Mohanasubha, M. Senthilvelan, M. Lakshmanan
Summary: This paper addresses the challenging problem of identifying higher dimensional nonlinear ordinary differential equations (ODEs) that possess a Lagrangian structure. The authors propose a systematic algorithmic procedure to determine the Lagrangian by obtaining a set of constraints in the form of Helmholtz conditions for a system of two coupled second-order ODEs. The analysis is demonstrated using appropriate examples.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Interdisciplinary Applications
M. Manoranjani, D. V. Senthilkumar, V. K. Chandrasekar
Summary: We analyze the behavior of Kuramoto oscillators coupled via an adaptive mean-field variable and identify distinct phase transitions in different ranges of the time-scale parameter. We derive the evolution equations for the macroscopic order parameters and find consistent results with the observed dynamical transitions.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Fluids & Plasmas
S. Stalin, R. Ramakrishnan, M. Lakshmanan
Summary: In this paper, the authors study the dynamics of a class of interesting vector solitons in the long-wave-short-wave resonance interaction system. They derive nondegenerate vector soliton solutions using the Hirota bilinear method and express the solutions in a compact form using Gram-determinants. The authors also analyze the collision scenarios of the solitons and point out the shape-changing behavior of the nondegenerate solitons, which has not been observed in the already known vector solitons.
Article
Physics, Fluids & Plasmas
S. Thamizharasan, V. K. Chandrasekar, M. Senthilvelan, Rico Berner, Eckehard Schoell, D. Senthilkumar
Summary: This study investigates an adaptive network where the connection weights coevolve with the dynamical states of the local nodes influenced by an external stimulus. The adaptive network exhibits various exotic dynamical states under external forcing, including itinerant chimera states, bump states, and bump frequency cluster states. Measures for the strength of incoherence are introduced and a phase diagram illustrating the range of dynamical states is provided.
Article
Physics, Fluids & Plasmas
Snehasish Roy Chowdhury, Ramesh Arumugam, Wei Zou, V. K. Chandrasekar, D. Senthilkumar
Summary: This article investigates the influence of limiting dispersal on the stability of a metacommunity. The study finds that limiting predator dispersal decreases the spread of asynchronous states, while limiting prey dispersal promotes the spread of inhomogeneous steady states. Additionally, the research shows that the effects of limiting dispersal vary at different spatial scales.