Related papers: Synchronization hypothesis in the Winfree model
Synchronization of self-sustained oscillators under fixed-frequency and amplitude forcing is well understood, but how time-varying forcing mangles phase locking has been much less explored. Theory predicts that slow, deterministic…
In principle, while coupled limit cycle oscillators can overcome mismatch in intrinsic rates and match their frequencies, but zero phase lag synchronization is just achievable in the limit of zero mismatch, i.e., with identical oscillators.…
We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…
Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a…
We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven…
We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations…
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…
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.
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
This paper addresses important control and observability aspects of the phase synchronization of two oscillators. To this aim a feedback control framework is proposed based on which issues related to master-slave synchronization are…
We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of…
We study the manifestation of antiphase synchronization in a system of n Rossler Oscillators coupled through a dynamic environment. When the feedback from system to environment is positive (negative) and that from environment to system is…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
Coupled distinct arrays of nonlinear oscillators have been shown to have a regime of high frequency, or ultra-harmonic, oscillations that are at multiples of the natural frequency of individual oscillators. The coupled array architectures…
The phenomenon of phase synchronization of oscillatory systems arising out of feedback coupling is ubiquitous across physics and biology. In noisy, complex systems, one generally observes transient epochs of synchronization followed by…
Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly…
We study the Kuramoto model for coupled oscillators. For the case of identical natural frequencies, we give a new proof of the complete frequency synchronization for all initial data; extending this result to the continuous version of the…
A major open question in the study of synchronization of coupled oscillators is to find necessary and sufficient condition for a system to synchronize on a given family of graphs. This is a difficult question that requires to understand…
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…
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…