相关论文: Renewal Approach to the Analysis of the Asynchrono…
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…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate 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…
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…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
We propose a population model for $\delta$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term.…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
In this article I investigate the novel synchronization behaviors of evolving pulse-coupled oscillator networks. Unlike previous models, the time-varying mechanism is inspired by neural network development, where seldom used links die out…
This technical note deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of the their phase response function. The network of pulse coupled…
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…
The property of desynchronization in an all-to-all network of homogeneous impulse-coupled oscillators is studied. Each impulse-coupled oscillator is modeled as a hybrid system with a single timer state that self-resets to zero when it…
The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically…
The amplitude-dependent frequency of the oscillations, termed \emph{nonisochronicity}, is one of the essential characteristics of nonlinear oscillators. In this paper, the dynamics of the Rossler oscillator in the presence of…
Pulse-coupled threshold units serve as paradigmatic models for a wide range of complex systems. When the state variable of a unit crosses a threshold, the unit sends a pulse that is received by other units, thereby mediating the…
Synchronization is an important dynamical phenomenon in coupled nonlinear systems, which has been studied extensively in recent years. However, analysis focused on individual orbits seems hard to extend to complex systems while a global…
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of non-classical steady states.…
The stability of synchronous states is analysed in the context of two populations of inhibitory and excitatory neurons, characterized by different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable…
We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…