Article
Computer Science, Interdisciplinary Applications
Hongwei Zhu, Qionglin Dai, Haihong Li, Junzhong Yang
Summary: In this paper, the authors study the effects of parameter heterogeneity on the coupling dynamics of three coupled Lorenz oscillators. It is found that in the presence of parameter heterogeneity, the complete synchronous state is replaced by lag synchronous state with the same Lyapunov exponent as the complete synchronous chaos. Two types of oscillation quenching states, homogeneous nontrivial equilibria and heterogeneous equilibria, are observed depending on the coupling strength. The transition among lag synchronous state and different types of quenching states is found to be discontinuous.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
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
Physics, Multidisciplinary
Amirhossei Nazerian, Shirin Panahi, Francesco Sorrentino
Summary: This perspective discusses the synchronization in networks of coupled non-phase oscillators in the presence of parametric mismatches. It explains that when there are small parametric mismatches, the stability conditions for the synchronous solution are the same as in the case of identical oscillators, but the synchronization error increases with the size of the mismatches. In the case of larger parameter mismatches, it provides an explanation for why parameter mismatches sometimes hinder and sometimes enhance stability of the synchronous solution.
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
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
Tina Verma, Arvind Kumar Gupta
Summary: Connectivity and rates of movement play a significant role in the spread of infectious diseases, with diseases like COVID-19 spreading rapidly. The SEIR epidemic model provides insights into the transmission of infected individuals across different patches.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Wei Zou, Sujuan He, Chenggui Yao
Summary: This paper investigates the stability of amplitude death in conjugate-coupled Stuart-Landau oscillators. It is found that frequency mismatch has no impact on the stability, which is solely determined by the mean frequency. Analytic equations for the continuous and discrete spectra are derived for a mean-field system of conjugate-coupled oscillators, defining the stability of amplitude death in the thermodynamic limit. The explicit calculation of amplitude death boundaries is presented for the Lorentzian frequency distribution. It is proven that amplitude death in networked oscillators with conjugate coupling is topology-free.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Engineering, Mechanical
Roeland Wildemans, Viktor Kornilov, Ines Lopez Arteaga
Summary: A nonlinear phenomenological model consisting of two coupled oscillators is proposed to describe the rich nonlinear behavior of a simple combustion system. The model accurately reproduces the different observed regimes, including supercritical Hopf bifurcation, limit cycle, quasi-periodic, and period-2 limit cycle oscillations. Parameter estimation shows a good quantitative match between the model response and experimental data, suggesting that the model effectively captures the nonlinear self-excited acoustic behavior of premixed flames.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Nannan Zhao, Xuexue Zhang
Summary: Extensive studies have shown that higher-order many-body interactions can facilitate the onset of amplitude death (AD) dynamics in oscillatory systems. In this work, we investigate the impacts of first-order (pairwise) and second-order (three-body) interactions on the emergence of AD in a simplicial complex of coupled Stuart-Landau oscillators. We find that AD can be achieved by either first-order or second-order interactions, with the latter requiring a lower coupling strength.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Automation & Control Systems
Tomas Gedeon, Breschine Cummins
Summary: This work investigates the emergent behavior of coupled biochemical oscillators and reveals the phenomenon of oscillation continuation and cessation in different parameter regimes. These findings have important implications for understanding condition-dependent coupling and un-coupling of regulatory networks.
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS
(2023)
Article
Engineering, Mechanical
D. Premraj, Krishna Manoj, Samadhan A. Pawar, R. I. Sujith
Summary: The paper investigates the dynamic behavior of coupled Stuart-Landau oscillators with varying amplitude and frequency, finding that increasing the amplitude leads to the disappearance of amplitude death regions and observing an alternation between in-phase and anti-phase synchronization regions with higher values of time delay. Additionally, the introduction of frequency mismatch also affects the region of amplitude death.
NONLINEAR DYNAMICS
(2021)
Review
Physics, Multidisciplinary
Wei Zou, D. Senthilkumar, Meng Zhan, Jurgen Kurths
Summary: The study of rhythmic behaviors in coupled dynamical networks is an active and rapidly evolving field, covering various aspects from oscillation quenching to reviving. These investigations provide vital insights into the collapse and revival of macroscopic rhythmic behaviors, enhancing our understanding of evading irreversible failures of coupled dynamical networks.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2021)
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
Physics, Multidisciplinary
Jiangsheng Wang, Changgui Gu, Peng Ji
Summary: This study introduces a new mechanism to induce first-order phase transitions in coupled oscillators through frequency-amplitude correlation, providing a new perspective on understanding explosive phenomena.
NEW JOURNAL OF PHYSICS
(2022)
