Related papers: Collective Phase Sensitivity
We prove that a group of injection-locked oscillators, each modelled using a nonlinear phase macromodel, responds as a single oscillator to small external perturbations. More precisely, we show that any group of injection-locked oscillators…
We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…
Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a…
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this…
We consider a population of globally coupled oscillators driven by common noise. By applying the Ott-Antonsen ansatz and by averaging over the fast oscillations, we obtain analytically tractable equations for the noisy evolution of the…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
Many real oscillators are coupled to other oscillators and the coupling can affect the response of the oscillators to stimuli. We investigate phase response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked…
We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the…
A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is…
We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…
We present an analytical and numerical study of the coherent exciton polarization including exciton-exciton correlation. The time evolution after excitation with ultrashort optical pulses can be divided into a slowly varying polarization…
We present an efficient technique for control of synchrony in a globally coupled ensemble by pulsatile action. We assume that we can observe the collective oscillation and can stimulate all elements of the ensemble simultaneously. We pay…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal…
A system of two enzymes mechanically coupled to each other in a viscous medium was recently studied, and conditions for obtaining synchronization and an enhanced average rate of the thermally-activated catalytic reactions of the enzymes…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…
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…
Understanding the origin of phase synchronization between quantum self-sustained oscillators has garnered significant interest in recent years. In this work, we study phase synchronization in three settings: between two continuous-variable…
We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from…
We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the…