Related papers: Inferring Coupled Stuart-Landau Equations from Wav…
Numerous biological systems exhibit transitions to synchronised oscillations via a population-density-dependant mechanism known as quorum sensing. Here we propose a model system, based on spatially distributed limit-cycle oscillators, that…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation…
We study the weakly nonlinear saturation of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. This instability, established in our preceding work as a Hopf bifurcation of a…
We demonstrate mutual synchronization of Josephson oscillations in multiple stacks of intrinsic Josephson junctions of the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta }$. Detailed analysis of the full polarization parameters…
The dynamics of an ensemble of $N$ weakly coupled limit-cycle oscillators can be captured by their $N$ phases using standard phase reduction techniques. However, it is a phenomenological fact that all-to-all strongly coupled limit-cycle…
We report an interesting symmetry-breaking transition in coupled identical oscillators, namely the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the…
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…
Two decades ago, a phenomenon resembling Landau damping was described in the synchronization of globally coupled oscillators: the evidence of a regime where the order parameter decays when linear theory predicts neutral stability for the…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
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…
Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon it underpins the study of complex systems and has…
A data-driven model identification strategy is developed for dynamical systems near a supercritical Hopf bifurcation with nonautonomous inputs. This strategy draws on phase-amplitude reduction techniques, leveraging an analytical…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
Spatio-temporal chaos in parametrically driven waves is investigated in one and two dimensions using numerical simulations of Ginzburg-Landau equations. A regime is identified in which in one dimension the dynamics are due to double phase…
Distributed delays modeled by 'weak generic kernels' are introduced in the well-known coupled Landau-Stuart system, as well as a chaotic van der Pol-Rayleigh system with parametric forcing. The systems are close via the 'linear chain…
In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence…
In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is…
We present a set of phase-space portraits illustrating the extraordinary oscillatory possibilities of the dynamical systems through the so-called generalized Landau scenario. In its simplest form the scenario develops in N dimensions around…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous…