Related papers: Probabilistic Convergence Guarantees for Type II P…
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…
We explore systems of pulse-coupled oscillators beyond the mean-field limit [R.E. Mirollo and S.H. Strogatz, {SIAM J. Appl. Math.} {\bf 50}, 1645 (1990)] by means of a manageable description which leads to a great simplification of the…
By spreading phases on the unit circle, desynchronization algorithm is a powerful tool to achieve round-robin scheduling, which is crucial in applications as diverse as media access control of communication networks, realization of…
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…
Decentralized heading control is crucial for robotic network operations such as surveillance, exploration, and cooperative construction. However, few results consider decentralized heading control when the speed of heading adjustment is…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions---subsets of the phase space filled…
Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to total synchronization. We are able to develop exact solutions for…
We present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases…
This paper addresses the synchronization rate of weakly connected pulse-coupled oscillators (PCOs). We prove that besides coupling strength, the phase response function is also a determinant of synchronization rate. Inspired by the result,…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
We study the reliability of spike output in a general class of pulse-coupled oscillators receiving a fluctuating input. Showing that this problem is equivalent to noise-induced synchronization between identical networks of oscillators, we…
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.
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized.…
Sufficient conditions for synchronization of coupled Lienard-type oscillators are investigated via averaging technique. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the…
We study the dynamical behavior of an ensemble of oscillators interacting through short range bidirectional pulses. The geometry is 1D with periodic boundary conditions. Our interest is twofold. To explore the conditions required to reach…
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…
We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations…
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…