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When two systems are coupled, the driver system can function as an external forcing over the driven or response system. Also, an external forcing can independently perturb the driven system, leading us to examine the interplay between the…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
In a quasi-1D thermal convective system consisting of a large array of nonlinearly coupled oscillators, clustering is the way to achieve a regime of mostly antiphase synchronized oscillators. This regime is characterized by a spatiotemporal…
We investigate numerically the clustering behavior of a system of phase oscillators with positive and negative couplings under a periodic external driving field with a bimodal distribution of driving phases. The phase distribution and the…
We improve current instability-based methods for the selection of the number of clusters $k$ in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
A model of clustering dynamics is proposed for a population of spatially distributed active rotators. A transition from excitable to oscillatory dynamics is induced by the increase of the local density of active rotators. It is interpreted…
Dipolar spin ensembles with random spin positions attract much attention currently because they help to understand decoherence as it occurs in solid state quantum bits in contact with spin baths. Also, these ensembles are systems which may…
We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
A symmetry breaking mechanism is shown to occur in an array composed of symmetric bistable Lorenz units coupled through a nearest neighbour scheme. When the coupling is increased, we observe the route: standing --> oscillating -->…
Globally coupled oscillator systems with inertia exhibit complex synchronization patterns, among which the emergence of a couple of secondary synchronized clusters (SCs) in addition to the primary cluster (PC) is especially distinctive.…
We revisit the problem of quantum bi- and multi-stability by considering the dissipative Double Resonance Model. For a large driving frequency, this system has a simpler phase structure than the driven dissipative nonlinear oscillator --…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
A theoretical framework is developed for a precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the…
Gravitational clustering in the nonlinear regime remains poorly understood. Gravity dual of gravitational clustering has recently been proposed as a means to study the nonlinear regime. The stable clustering ansatz remains a key ingredient…
A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability…