Related papers: Weakly Coupled Oscillators in a Slowly Varying Wor…
We investigate globally coupled stochastic three-state oscillators, which we consider as general models of stochastic excitable systems. We compare two situations:in the first case the transitions between the three states of each unit…
We report a new experimental approach using an optoelectronic feedback loop to investigate the dynamics of oscillators coupled on large complex networks with arbitrary topology. Our implementation is based on a single optoelectronic…
Phase-space analysis has been widely used in the past for the study of optical resonant systems. While it is usually employed to analyze the far-field behaviour of resonant systems we focus here on its applicability to coupling problems. By…
Synchronization by exchange of pulses is a widespread phenomenon, observed in flashing fireflies, applauding audiences and the neuronal network of the brain. Hitherto the focus has been on integrate-and-fire oscillators. Here we consider…
We propose a general method for optimizing periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators based on phase reduction and nonlinear programming. We derive averaged phase dynamics from the mathematical…
We consider networks of weakly pulse-coupled identical oscillators. In an effort to resolve a long-standing problem, we develop an analytic condition on the infinitesimal phase response curve (iPRC) for synchronized dynamic behaviour,…
We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can…
Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional…
Neuro-inspired computing architectures are one of the leading candidates to solve complex, large-scale associative learning problems. The two key building blocks for neuromorphic computing are the synapse and the neuron, which form the…
This paper presents new methods and results on almost global synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any…
In a noisy environment, oscillations loose their coherence which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional…
This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on delayed interactions with linear and quadratic terms.…
In order to study the possible phase conjugation of optical near-fields, it is necessary to go beyond the slowly varying envelope- and electric dipole approximations that are normally applied in phase conjugation studies where spatially…
We suggest a definition for a type of chimera state that appears in networks of indistinguishable phase oscillators. Defining a "weak chimera" as a type of invariant set showing partial frequency synchronization, we show that this means…
We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of…