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Synchronization of coupled oscillators is observed in many natural and engineered systems and emerges due to the interactions within the system. It can be both beneficial, e.g., in power grids, and harmful, e.g., in epileptic seizures. In…
The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing,…
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of non-classical steady states.…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
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 long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range…
We present a phenomenological reduced-order model to capture the transition to thermoacoustic instability in turbulent combustors. The model is based on the framework of synchronization and considers the acoustic field and the unsteady heat…
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…
We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…
We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and time-varying (e.g., due to…
We consider optimization of linear stability of synchronized states between a pair of weakly coupled limit-cycle oscillators with cross coupling, where different components of state variables of the oscillators are allowed to interact. On…
Phase synchronization between collective oscillations exhibited by two weakly interacting groups of non-identical phase oscillators with internal and external global sinusoidal coupling of the groups is analyzed theoretically. Coupled…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response.…
Coupled non-linear oscillators are ubiquitous in dynamical studies. A wealth of behaviors have been found mostly for globally coupled systems. From a complexity perspective, less studied have been systems with local coupling, which is the…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…
We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over $d$-dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored…