Related papers: Synchronizing pulse-coupled oscillators by constra…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of inter-event density allows for a self-consistent calculation that determines the…
Driven by increased applications in biological networks and wireless sensor networks, synchronization of pulse-coupled oscillators (PCOs) has gained increased popularity. However, most existing results address the local synchronization 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…
We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed…
We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes…
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 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…
Phase response functions are the central tool in the mathematical analysis of pulse-coupled oscillators. When an oscillator receives a brief input pulse, the phase response function specifies how its phase shifts as a function of the phase…
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators…
We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. Events emerging from the networks may form an oscillatory behavior or may…
A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations…
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…
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…
We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
We consider the integrate-and-fire model of the cardiac pacemaker with delayed pulsatile coupling. Sufficient conditions of synchronization are obtained for identical and non-identical oscillators.
Clock synchronization is a widely discussed topic in the engineering literature. Ensuring that individual clocks are closely aligned is important in network systems, since the correct timing of various events in a network is usually…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…
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…