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Synchronization of forced reactively coupled van der Pol oscillators is investigated in the phase approximation. We discuss essential features of the reactive coupling. Bifurcation mechanisms for the destruction of complete synchronization…
The paper revisits recently revealed regimes of the "nonconventional synchronization" in systems of coupled bi-stable Van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges…
In addition to a common synchronization and/or localization behavior, a system of linearly coupled identical bistable Van der Pol (BVdP) oscillators can exhibit a "non-conventional" or "modal" synchronization. In two-DOF case, one can…
Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work,…
Recently, the synchronization of coupled quantum oscillators has attracted a great deal of interest. Synchronization requires driven constituents, and in such systems, the coupling can be designed to be nonreciprocal. Nonreciprocally…
The particular properties of dynamics are discussed for the dissipatively coupled van der Pol oscillators, non-identical in values of parameters controlling the Hopf bifurcation. Possibility of a special synchronization regime in an…
We report the observation of a novel and non-trivial synchronization state in a system consisting of three oscillators coupled in a linear chain. For certain ranges of coupling strength the weakly coupled oscillator pair exhibits phase…
The particular properties of synchronization are discussed for coupled auto-oscillating systems, which are characterized by non-quadratic law of potential dependence on the coordinate. In particular, structure of the parameter plane…
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…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive or repulsing. We develop an analytical approach based on a transformation to approximate…
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
We study the influence of telegraph noise on synchrony of limit cycle oscillators. Adopting the phase description for these oscillators, we derive the explicit expression for the Lyapunov exponent. We show that either for weak noise or…
Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to…
Limit cycles (attractors for neighbouring periodic orbits in a dissipative dynamical system) have been widely studied but the corresponding generalization for quasi periodic orbits have rarely been discussed. Here we investigate "higher…
In this paper, a numerical study on the complete synchronization phenomenon exhibited by coupled forced negative conductance circuits is presented. The nonlinear system exhibiting two types of chaotic attractors is studied for complete…
This note addresses the output synchronization problem of incrementally output-feedback passive nonlinear systems in the presence of exogenous disturbances. Two kinds of distributed controllers are proposed; one placed at the nodes and the…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…