Related papers: Approximate solution for the oscillation death sta…
A parametrically driven oscillator has two stable vibrational states at half the modulation frequency. The states have opposite phase and equal amplitudes. An extra drive at half the modulation frequency provides an effective bias that…
We introduce a model to study the effect of degree-frequency correlations on synchronization in networks of coupled oscillators. Analyzing this model, we find several remarkable characteristics. We find a stationary synchronized state that…
We consider a system of coupled oscillators with finite inertia and time-delayed interaction, and investigate the interplay between inertia and delay both analytically and numerically. The phase velocity of the system is examined; revealed…
A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is…
In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation…
We propose a generalized matrix-valued synchronization model which can be regarded as matrix generalization of the classical Winfree model to the special orthogonal group, and we provide several sufficient frameworks leading to the emergent…
Most previous studies on coupled dynamical systems assume that all interactions between oscillators take place uniformly in time, but in reality, this does not necessarily reflect the usual scenario. The heterogeneity in the timings of such…
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…
This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
We show that oscillation death as a specific type of oscillation suppression, which implies symmetry breaking, can be controlled by introducing time-delayed coupling. In particular, we demonstrate that time delay influences the stability of…
Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest-state, therefore quenching their oscillation. This phenomenon is termed "amplitude death". Well-known and studied in classical self-oscillators, amplitude…
Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
Cyclic motions in vertebrates, including heart beating, breathing and walking, are derived by a network of biological oscillators having fascinating features such as entrainment, environment adaptation, and robustness. These features…
We study the conditions of amplitude death in a network of delay-coupled limit cycle oscillators by including time-varying delay in the coupling and self-feedback. By generalizing the master stability function formalism to include…
The dynamics of an ensemble of $N$ weakly coupled limit-cycle oscillators can be captured by their $N$ phases using standard phase reduction techniques. However, it is a phenomenological fact that all-to-all strongly coupled limit-cycle…
We study the emergence of phase-locking for Winfree oscillators under the effect of inertia. It is known that in a large coupling regime, oscillators governed by the deterministic second-order Winfree model with inertia converge to a unique…
We study the death and restoration of collective oscillations in networks of oscillators coupled through random-walk diffusion. Differently than the usual diffusion coupling used to model chemical reactions, here the equilibria of the…
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…