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Coupled oscillators can serve as a testbed for larger questions of pattern formation across many areas of science and engineering. Much effort has been dedicated to the Kuramoto model and phase oscillators, but less has focused on…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths or inhomogeneous natural frequencies. The solutions show remarkable profiles of phase lags from the pacemaker corresponding to the ratio of upward…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…
We investigate the occurrence of collective dynamical states such as transient amplitude chimera, stable amplitude chimera and imperfect breathing chimera states in a \textit{locally coupled} network of Stuart-Landau oscillators. In an…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
We reduce the dynamics of an ensemble of mean-coupled Stuart-Landau oscillators close to the synchronized solution. In particular, we map the system onto the center manifold of the Benjamin-Feir instability, the bifurcation destabilizing…
We study the collective dynamics of coupled Stuart--Landau oscillators, which model limit-cycle behavior near a Hopf bifurcation and serve as the amplitude-phase analogue of the Kuramoto model. Unlike the well-studied phase-reduced systems,…
We study synchronization in a system of Stuart-Landau oscillators with frequency-weighted coupling. For three typical unimodal frequency distributions, namely, the Lorentzian, the triangle, and the uniform, we found that the first-order…
The dynamics of two active nonlinear resonators coupled to a linear resonator is studied theoretically. Possible stationary states and its dynamical stability are considered in detail. The spontaneous symmetry breaking is found and it is…
This paper addresses the behavior of large systems of heterogeneous, globally coupled oscillators each of which is described by the generic Landau-Stuart equation, which incorporates both phase and amplitude dynamics of individual…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
We present a data-driven framework to infer phase-amplitude equations of coupled limit-cycle oscillators directly from waveform measurements. Exploiting the universality of the Stuart-Landau normal form near a supercritical Hopf…
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…
The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
We study nonlinear dynamics in a system of two coupled oscillators, describing the motion of two interacting microbubble contrast agents. In the case of identical bubbles, the corresponding symmetry of the governing system of equations…