Article
Mathematics, Applied
Yao Xu, Qi Wang, Wenxue Li, Jiqiang Feng
Summary: This paper investigates the stability and synchronization problems of fractional-order delayed multilink complex networks with nonlinear hybrid couplings, considering both discrete time-varying delays and distributed time-varying delays. Criteria are established under feedback control using graph-theoretic approach and Lyapunov method, related to the topological structure of subsystems, control gain, and the upper bound of time-varying delays. The practicality of the results is demonstrated on specific neural networks and chaotic systems, and numerical examples show the effectiveness and feasibility of the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Multidisciplinary Sciences
T. Y. Zheng, W. H. Yang, J. Sun, X. Y. Xiong, Z. T. Li, X. D. Zou
Summary: Reservoir computing is a computational framework inspired by biology that excels in processing temporal data due to its derivation from recurrent neural networks. While known for its fast and effective training scheme and easy hardware implementation, it is also sensitive to the optimization of architectural parameters. The article presents a time-delayed RC with a single clamped-clamped silicon beam resonator exhibiting Duffing nonlinearity, and introduces an optimization method based on Bifurcation Point Frequency Modulation (BPFM) to find the optimal driving frequency.
SCIENTIFIC REPORTS
(2021)
Article
Engineering, Mechanical
Gao Hong, Deng Zhongmin, Zhao Yanlin, Yan Hongbo, Zhang Xinjie, Meng Lingzi, Luo Qi
Summary: In this study, a time-delayed displacement and velocity feedback controller was designed to improve the nonlinear dynamic characteristics and stability of a giant magnetostrictive actuator system. The results showed that the velocity feedback gain and time delay parameters had a significant impact on the stability of the primary resonance, chaotic motion, and limit cycle amplitude.
NONLINEAR DYNAMICS
(2022)
Article
Multidisciplinary Sciences
Ali Momeni, Romain Fleury
Summary: This article introduces an analog neuromorphic platform for optical wave-based machine learning, which is characterized by energy efficiency, speed, and scalability. By utilizing time-Floquet physics to induce strong non-linear entanglement between signal inputs at different frequencies, the authors successfully solve complex neuromorphic computing tasks.
NATURE COMMUNICATIONS
(2022)
Article
Automation & Control Systems
Yuan-Guang Zheng, Ming-Huan Liu
Summary: Dynamic time-delayed feedback control (DDFC) is applied to stabilize the unstable periodic orbits (UPOs) of chaotic systems, improving control effectiveness by expanding the stability domain and optimizing control objectives.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
V. P. Vera-avila, J. R. Sevilla-Escoboza, R. R. Rivera Duron, J. M. Buldu
Summary: The phenomenon of dynamical consistency in a network of nonlinear oscillators was investigated both numerically and experimentally. Dynamical consistency refers to the ability of a dynamical system to respond in the same way when perturbed by the same external signal. The study focused on certain dynamical systems connected through a non-regular network, exploring synchronization and consistency arising from varying coupling strengths within the network.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Artificial Intelligence
Juan-Juan He, Hui Chen, Ming-Feng Ge, Teng-Fei Ding, Leimin Wang, Chang-Duo Liang
Summary: This paper investigates the finite-time synchronization problem of complex dynamical networks with quantized time-varying delayed couplings and adaptive coupling strengths, and develops a novel finite-time adaptive quantized control algorithm. Sufficient conditions for finite-time synchronization are derived using convex combination technique and nonsmooth analysis, and numerical simulations verify the effectiveness and feasibility of the proposed algorithm.
Article
Engineering, Mechanical
Meiling Xie, Derui Ding, Guoliang Wei, Xiaojian Yi
Summary: This study investigates the fusion estimation problem of sensor networks for nonlinear time-varying systems with energy constraints, time delays, and packet loss. A novel transmission model with energy constraints and a method utilizing Lyapunov stability theory to establish conditions are proposed to ensure predetermined performance. The desired gains of local estimators and suboptimal fusion weight matrices are obtained through the solution of linear matrix inequalities.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Fluids & Plasmas
Jason Czak, Michel Pleimling
Summary: This study demonstrates that selectively perturbing part of a system can generate new space-time patterns that are not observed when controlling the entire system. These patterns may emerge either in the perturbed or unperturbed regions, showing stability and possibly perfect periodicity. The mechanism underlying the observed pattern generation is related to diffusion across the interfaces separating the perturbed and unperturbed regions.
Article
Engineering, Multidisciplinary
Liangliang Li, Wenlin Jiang, Zhengwen Tu
Summary: This paper discusses the problem of saturated impulsive control of nonlinear complex dynamical networks with different delays on hybrid time domains. Firstly, an exponential estimated inequality of delayed dynamical system on time scales is derived. Secondly, combining with time scale theory, comparison principle and matrix measure, some different exponential scale-type synchronization conditions for delayed nonlinear complex networks on hybrid time domains under saturated impulsive controller are given. Further, the impulsive input is constrained by the saturation constraint. Finally, three examples with different time domains are given to prove the validity of our results.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Automation & Control Systems
Jin-Liang Wang, Lu Wang, Huai-Ning Wu
Summary: This article investigates the synchronization problem for directed and undirected complex networks with multiple state or delayed state couplings, subject to recoverable attacks. Synchronization criteria are established using Lyapunov functional, inequality techniques, and state-feedback controller. The article also discusses the synchronization of networks with multiple delayed state couplings.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Applied
Qian Cui, Lulu Li, Lei Wang
Summary: This paper focuses on the stability of delayed nonlinear systems (DNSs) under state dependent delayed impulses (SDDIs). Firstly, it proves that the pulse phenomenon can be avoided under certain assumptions. Then, new theoretical frameworks are established for the stability of DNSs under state dependent delayed impulsive control and delayed impulsive interference through the method of comparison principle. Furthermore, these criteria are applied in analyzing the stability of delayed neural networks (DNNs) under SDDIs. Finally, examples are provided to demonstrate the validity of the obtained results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Automation & Control Systems
Mingzhu Wang, Shuchen Wu, Xiaodi Li
Summary: This paper investigates Lyapunov stability of general nonlinear systems using event-triggered impulsive control, considering delayed impulses. By excluding Zeno behavior, a set of sufficient conditions for uniform and asymptotic stability are obtained based on impulsive control theory in the framework of event triggering. The results depend on the event-triggering mechanism and time delays.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Automation & Control Systems
Zongying Li, Xu Xu, Tingruo Yan, Eric Li
Summary: This paper investigates fixed-time leader-following synchronization in a non-identical delayed network using non-chattering nonlinear control. By introducing a function of control error, a continuous and differential controller is constructed without using the sign function and absolute value of the error. Sufficient conditions are established to guarantee that synchronization errors converge exactly to zero within a fixed time interval. The proposed approach provides high convergence for accurately tracking the leader's trajectory, and eliminates chattering effects through obtaining a tighter bound for the settling time.
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
(2022)
Article
Automation & Control Systems
Shuchen Wu, Xiaodi Li
Summary: In this paper, the finite-time stability of nonlinear systems with delayed impulses is studied using the Lyapunov method. The relationship among system structure, delayed impulses, and settling time is established, and sufficient conditions for finite-time stability are presented. The design methods of impulse time sequence for stabilizing and destabilizing impulses with time delays are proposed, and the impacts of delayed impulses on the settling time estimation are analyzed. Two numerical examples are provided to illustrate the analysis.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Physics, Multidisciplinary
Rico Berner, Simon Vock, Eckehard Schoell, Serhiy Yanchuk
Summary: The study developed a master stability approach for a wide class of adaptive networks, simplifying the synchronization problem to a low-dimensional system and revealing the interplay between adaptivity and network structure in the formation of stability islands and complex synchronization patterns.
PHYSICAL REVIEW LETTERS
(2021)
Article
Mathematics, Applied
Vander L. S. Freitas, Serhiy Yanchuk, Michael Zaks, Elbert E. N. Macau
Summary: The study has shown that autonomous mobile agents can form symmetric clusters in specific regions of parameter space and proposes a strategy for switching formation modes. In addition, a method for obtaining chaotic almost-circular trajectories and symmetric clusters with non-overlapping particles is introduced.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Rico Berner, Serhiy Yanchuk, Yuri Maistrenko, Eckehard Schoell
Summary: The article introduces a special subclass of generalized m-splay states that typically manifest incoherent dynamics in networks. Explicit linear stability conditions for splay states are provided for a general class of phase oscillator networks, exemplified with the Kuramoto-Sakaguchi model. The simplicity and applicability of the stability conditions to networks of arbitrary size are highlighted.
Article
Physics, Multidisciplinary
Vander L. S. Freitas, Serhiy Yanchuk, Helder L. C. Grande, Elbert E. N. Macau
Summary: The study highlights the significant impact of time-delay and phase lag on circular formations with symmetric clusters, potentially leading to unstable arrangements when the time-delay exceeds a critical value. By controlling the phase lag, the formation morphology can be effectively manipulated, even resulting in more complex stable arrangements.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Mathematics, Applied
Braden Thorne, Thomas Jungling, Michael Small, Debora Correa, Ayham Zaitouny
Summary: Reservoir Time Series Analysis (RTSA) is a method that uses the state space representation generated by a reservoir computing model for time series analysis, showing superior performance in feature distinction and accuracy compared to benchmark methods.
Article
Mathematics
Serhiy Yanchuk, Matthias Wolfrum, Tiago Pereira, Dmitry Turaev
Summary: This paper presents criteria for the absolute stability of delay differential equations (DDEs) with discrete time-delays and establishes the equivalence between absolute stability and asymptotic stability for different delay scenarios. The necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays are also provided, which are crucial for understanding bifurcations caused by varying time delays.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Computer Science, Artificial Intelligence
Thomas Jungling, Thomas Lymburn, Michael Small
Summary: This study investigates the propagation and distribution of information-carrying signals injected in dynamical systems acting as reservoir computers. By using multivariate correlation analysis, measures known as the consistency spectrum and consistency capacity were revealed to be high-dimensional portraits of the nonlinear functional dependence between input and reservoir state. A hierarchy of capacities characterizes the interference of signals from each source, while time-resolved capacities form a profile of the reservoir's nonlinear fading memory for individual inputs.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Editorial Material
Neurosciences
Joana Cabral, Viktor Jirsa, Oleksandr V. Popovych, Alessandro Torcini, Serhiy Yanchuk
FRONTIERS IN SYSTEMS NEUROSCIENCE
(2022)
Article
Engineering, Mechanical
Daniel Maia, Juergen Kurths, Serhiy Yanchuk
Summary: This paper considers the synchronization problem of dynamical networks with delayed interactions. The focus is on stabilizing synchronous equilibria in regular networks with equal degrees of all nodes. Necessary and sufficient conditions for stabilization are obtained by studying such control near a Hopf bifurcation. It is found that the stabilization domains in the parameter space reappear periodically with time-delay, and the frequency of reappearance is linearly proportional to the number of cycle multipartitions of the network.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Max Thiele, Rico Berner, Peter A. A. Tass, Eckehard Schoell, Serhiy Yanchuk
Summary: This study presents a framework for describing the emergence of recurrent synchronization in complex networks with adaptive interactions. The phenomenon is manifested by temporal episodes of coherent and incoherent dynamics that alternate recurrently. Asymmetric adaptation rules and temporal separation between adaptation and individual node dynamics are identified as key features for the emergence of recurrent synchronization.
Article
Computer Science, Artificial Intelligence
Felix Koester, Serhiy Yanchuk, Kathy Ludge
Summary: This study demonstrates that delay-based reservoir computers can be characterized by a universal master memory function (MMF) and provides linear memory capacity. An analytical description of the MMF is proposed for efficient computing and can be applied to various reservoir scenarios.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Mathematics, Applied
Matthias Wolfrum, Serhiy Yanchuk, Otti D'Huys
Summary: In this study, the mechanisms for the appearance of multiple coexisting partially locked states in the Kuramoto-Sakaguchi system were fully analytically explained, along with the stability characteristics of these states and the role of the Sakaguchi phase lag parameter under different delay conditions.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Rico Berner, Volker Mehrmann, Eckehard Schoell, Serhiy Yanchuk
Summary: Multiplex networks consist of multiple layers with the same number of nodes and diagonal adjacency matrices between layers. This study focuses on a special class of multiplex networks where adjacency matrices for each layer can be simultaneously triangularized. A generalized master stability approach is proposed for a simplified description of stability of synchronized solutions in multiplex networks.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2021)
Article
Optics
Giovanni Giacomelli, Serhiy Yanchuk, Antonio Politi
Summary: This paper presents an approach that simplifies the dynamics by removing spatial dependence, accurately reproducing the phenomena described by the Maxwell-Bloch equations.
Article
Engineering, Multidisciplinary
S. Vock, R. Berner, S. Yanchuk, E. Schoell
Summary: Synchronization of networks of oscillatory units is an emergent phenomenon observed in various systems, with adaptively coupled oscillators exhibiting different synchronization phenomena such as hierarchical multifrequency clusters, traveling waves, or chimera states. The study analyzed the impact of random network topologies of varying dilution degrees on the robustness of multi-cluster states, and highlighted the interplay between adaptivity and topology using a master stability approach. Through this approach, the robustness of multifrequency cluster states against diluted connectivities can be illustrated.
