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The inspiration for this theoretical paper comes from recent experiments on a PT-symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators,…
We introduce a method to identify phase equations that include $N$-body interactions for general coupled oscillators valid far beyond the weak coupling approximation. This strategy is an extension of the theory from [Park and Wilson, SIADS…
Robust coordination and organization in large ensembles of nonlinear oscillatory units play a vital role in a wide range of natural and engineered system. The control of self-organizing network-coupled systems has recently seen significant…
We study the entanglement dynamics of two coupled mechanical oscillators, within a modulated optomechanical system. We find that, depending on the strength of the mechanical coupling, one could observe either a stationary or a dynamical…
We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation…
This paper is devoted to the study of the asymptotic dynamics of a class of coupled second order oscillators driven by white noises. It is shown that any system of such coupled oscillators with positive damping and coupling coefficients…
This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…
Many biological and chemical systems exhibit collective behavior in response to the change in their population density. These elements or cells communicate with each other via dynamical agents or signaling molecules. In this work, we…
We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry…
Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that…
A density oscillator is a fluid system in which oscillatory flow occurs between different density fluids through the pore connecting them. We investigate the synchronization in coupled density oscillators using two-dimensional hydrodynamic…
It has been found experimentally that when dc current is passed through a circuit consisting of two superconductors connected in parallel and reaches its critical value in one of the circuit branches the current in the branches undergoes…
We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the…
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on…
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…
The purpose of this paper to analyze in some detail the arguably simplest case of diversity-induced reseonance: that of a system of globally-coupled linear oscillators subjected to a periodic forcing. Diversity appears as the parameters…
This paper is concerned with the analysis of a class of impacting systems of relevance in applications: cam-follower systems. We show that these systems, which can be modelled as discontinuously forced impact oscillators, can exhibit…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
The Stuart-Landau oscillator generalized to $D > 2$ dimensions has SO($D$) rotational symmetry. We study the collective dynamics of a system of $K$ such oscillators of dimensions $D =$ 3 and 4, with coupling chosen to either preserve or…