Related papers: Phase-coupled Oscillators with Plastic Coupling: S…
We study the relationship between the partial synchronous (PaS) state and the coupling structure in general dynamical systems. By the exact proof, we find the sufficient and necessary condition of the existence of PaS state for the coupling…
The Kuramoto model captures various synchronization phenomena in biological and man-made systems of coupled oscillators. It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from…
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 study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…
A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
A model of two self-sustained oscillators interacting through memristive coupling is studied. Memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of…
We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention in the interplay between networks topological disorder and its synchronization features. Firstly, we analyze…
We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.
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 design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged.…
Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously when they are strongly…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive…
We consider $N$ oscillators coupled by a mean field as in the Winfree model. The model is governed by two parameters: the coupling strength $\kappa$ and the spectrum width $\gamma$ of the frequencies of each oscillator. In the uncoupled…
A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical…