Article
Mathematics, Applied
Shutong Liu, Zhongkui Sun, Nannan Zhao, Wei Xu
Summary: This paper investigates explosive transitions in a networked system, finding that different conditions can lead to different types of explosive transitions. Numerical observations reveal certain patterns related to the connections among the system, decay rates of dynamic environments, and intrinsic frequencies of subsystems.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
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
Mathematics, Applied
Erik T. K. Mau, Michael Rosenblum, Arkady Pikovsky
Summary: Phase reduction is a general approach for describing coupled oscillatory units by focusing on their phases. This paper presents a general framework for obtaining higher-order coupling terms in terms of the coupling parameter for two-dimensional oscillators with arbitrary coupling terms. The theory is applied to accurately predict Arnold's tongue phenomenon for the van der Pol oscillator using higher-order phase reduction.
Article
Automation & Control Systems
Jiayi Liu, Shuaihao Jiang, Yanbin Qu, Xuewei Zhang, Huihui Song
Summary: This paper discusses the global stability of coupled control systems (CCSs) and their application in microgrids. By using graph theory to construct a Lyapunov function and deriving stability criteria, the global asymptotical stability criterion for microgrids and sliding mode control method are proposed.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Wei Zou, Yuxuan Chen, D. V. Senthilkumar, Juergen Kurths
Summary: This study analyzes the phenomenon of oscillation quenching in diffusively coupled dynamical networks with inertia effects, and uncovers that even small inertia is capable of eradicating the onset of oscillation quenching.
Article
Mathematics, Interdisciplinary Applications
Zhongkui Sun, Shutong Liu, Nannan Zhao
Summary: This paper introduces a new type of transition process from oscillation to death state, called semi-explosive death, which is a mixture of half first order and half second order irreversible transition. The forward and backward second order transition points for this transition have been obtained theoretically and are in complete agreement with numerical results. The study also discusses the transition mechanisms between semi-explosive death and explosive death, along with the dependence on asymmetry factor and damping coefficient, both theoretically and numerically.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Lev Ryashko
Summary: Stochastic effects in corporate dynamics of two symmetrically coupled chaotic oscillators were studied. Increasing the coupling parameter changes the corporate deterministic dynamics and causes transitions between chaos-order-chaos. The study showed how the order window between Neimark-Sacker and crisis bifurcation points contracts and disappears with increasing noise.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Electrical & Electronic
Pezhman Kiani Vosta, Hossein Miar-Naimi, Mohsen Javadi
Summary: In this paper, a new method is introduced for calculating the oscillation amplitude of fourth-order oscillators using closed-form analytical equations. The method is applicable to all fourth-order oscillators and is independent of the oscillation frequency. The introduced method eliminates the need for complex and time-consuming simulations and helps designers understand design compromises for specific conditions.
INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
D. S. Shchapin, A. A. Emelianova, V. I. Nekorkin
Summary: A chaotic oscillation generator based on mixed dynamics is implemented on the FPGA, reproducing the dynamics of two adaptively coupled Kuramoto phase oscillators. It demonstrates oscillations corresponding to a chaotic attractor and a chaotic repeller, confirming the existence of mixed dynamics. The behavior of trajectories in phase space becomes more complex and the spectral characteristics change with a more uniform power distribution over the spectrum frequencies in the case of mixed dynamics.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Cong Liu, Zhi-Xi Wu, Chong-Yang Wang, Han-Xin Yang, Jian-Yue Guan
Summary: The study shows that astrocytes can listen to the talk between neurons, give advice, and contribute to heterogeneous couplings. The research focuses on the regulation function of astrocytes and explores the role of heterogeneous couplings among neuron-astrocyte components in signal response.
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, Applied
Sridevi Sriram, Karthikeyan Rajagopal, Anitha Karthikeyan, Akif Akgul
Summary: The network connectivities are crucial for exhibiting diverse collective dynamics in complex systems. Hindmarsh-Rose neurons connected by electromagnetic interactions are used to demonstrate different dynamical states and transitions. Specifically, the dynamical behaviors of the system are explored under regular, small-world, and random network connectivities. The results show that increasing coupling intensity leads to a transition from desynchronization to traveling wave state for all considered network interactions. Furthermore, the investigation is extended to a three-layer multiplex network where synchronization is achieved in all layers with increasing coupling intensity, eventually reaching a rest state at high coupling strength.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Electrical & Electronic
Juan Nunez, Jose M. Quintana, Maria J. Avedillo, Manuel Jimenez, Aida Todri-Sanial, Elisabetta Corti, Siegfried Karg, Bernabe Linares-Barranco
Summary: The study focuses on the implementation of oscillatory neural networks using VO2-based nano-oscillators, addressing key issues such as oscillator initialization and frequency synchronization.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Mathematics, Applied
Peter Ashwin, Christian Bick, Camille Poignard
Summary: This paper investigates the phenomenon of dead zones in dynamical systems, exploring conditions under which dead zones can emerge in coupled oscillators and applying these findings to coupled multiscale oscillators. The presence of dead zones in phase interactions functions can lead to interesting dynamical consequences for emergent dynamics.
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)
