Related papers: Multirhythmicity in an optoelectronic oscillator w…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
Macroscopic ensembles of radiating dipoles are ubiquitous in the physical and natural sciences. In the classical limit the dipoles can be described as damped-driven oscillators, which are able to spontaneously synchronize and collectively…
We investigate phase-locked solutions of a continuum field of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. Equilibrium relations for both synchronous and traveling wave solutions in the…
We investigate the stability of the synchronization manifold in a ring and an open-ended chain of nearest neighbors coupled self-sustained systems, each self-sustained system consisting of multi-limit cycles van der Pol oscillators. Such…
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…
We revisit the classical Suarez-Schopf delayed oscillator. Special attention is paid to the region of linear stability in the space of parameters. By means of the theory of inertial manifolds developed in our adjacent papers, we provide…
The logistic two-gene negative-feedback oscillator is locally asymptotically stable for all biological parameter values, since the trace of the Jacobian is uniformly negative. Real biological oscillators (circadian rhythms, the segmentation…
The plane-wave dynamics of 3*omega => (2*omega, omega) subharmonic optical parametric oscillators containing a second harmonic generator of the idler wave omega is analyzed analytically by using the meanfield approximation and numerically…
The Adler equation with time-periodic frequency modulation is studied. A series of resonances between the period of the frequency modulation and the time scale for the generation of a phase slip is identified. The resulting parameter space…
The interaction between a high-frequency dilational mode of a thin dielectric film and an optical cavity field is studied theoretically in the membrane-in-the-middle setup. A derivation from first principles leads to a multi-mode…
We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained…
We investigate entanglement in the above-threshold Optical Parametric Oscillator, both theoretically and experimentally, and discuss its potential applications to quantum information. The fluctuations measured in the subtraction of signal…
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…
We demonstrate that, in contrast with what was previously believed, multi-hump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves…
We propose a paradigmatic model system, a subcritical Hopf normal form subjected to noise and time-delayed feedback, to investigate the impact of time delay on coherence resonance in non-excitable systems. We develop analytical tools to…
We study a chain of $N+1$ phase oscillators with asymmetric but uniform coupling. This type of chain possesses $2^{N}$ ways to synchronize in so-called travelling wave states, i.e. states where the phases of the single oscillators are in…
In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both…
Quantum dot lasers display many unique dynamic phenomena when optically injected. Bistability has been predicted in a region of high injection strength. We show experimentally, rather than a phase-locked bistability, a square wave…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behaviour through a change of stability…