Related papers: Secure Synchronization of Heterogeneous Pulse-Coup…
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…
We show that a large class of pulse coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic…
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of…
A long-standing expectation is that two repulsively coupled oscillators tend to oscillate in opposite directions. It has been difficult to achieve complete synchrony in coupled identical oscillators with purely repulsive coupling. Here, we…
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…
We study the synchronization behavior of a noisy network in which each system is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all systems and can be generated by the environment or any…
The role of intermediaries in the synchronization of small groups of light controlled oscillators (LCO) is addressed. A single LCO is a two-time-scale phase oscillator. When pulse-coupling two LCOs, the synchronization time decreases…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…
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…
We introduce a system of pulse coupled oscillators that can change both their phases and frequencies; and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on…
We show that for pulse coupled oscillators a class of phase response curves with both excitation and inhibition exhibit robust convergence to synchrony on arbitrary aperiodic connected graphs with delays. We describe the basins of…
Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted…
We consider networks of weakly pulse-coupled identical oscillators. In an effort to resolve a long-standing problem, we develop an analytic condition on the infinitesimal phase response curve (iPRC) for synchronized dynamic behaviour,…
We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate…
This paper proposes a novel method to achieve and preserve synchronization for a set of connected heterogeneous Van der Pol oscillators. Unlike the state-of-the-art synchronization methods, in which a large coupling gain is applied to…
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…
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…
Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems.…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…
Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii)…