Related papers: Synchronization points: growth, asymptotics, congr…
In this paper we study spectral zeta functions associated to finite and infinite graphs. First we establish a meromorphic continuation of these functions under some general conditions. Then we study special values in the case of standard…
We study the effect of network topology on the collective dynamics of an oscillator ensemble. Specifically, we explore explosive synchronization in a system of interacting star networks. Explosive synchronization is characterized by an…
Spontaneous synchronization is a general phenomenon in which a large population of coupled oscillators of diverse natural frequencies self-organize to operate in unison. The phenomenon occurs in physical and biological systems over a wide…
In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data…
We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…
Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…
In many applications, such as sport tournaments or recommendation systems, we have at our disposal data consisting of pairwise comparisons between a set of $n$ items (or players). The objective is to use this data to infer the latent…
We study the $N$-point function of the density contrast to quadratic order in the squeezed limit during the matter-dominated (MD) and radiation-dominated (RD) eras in synchronous gauge. Since synchronous gauge follows the free-fall frame of…
Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior…
We study the asymptotic behavior of the cardinality of the fixed point set of iterates of an endomorphism of a complex torus. We show that there are precisely three types of behavior of this function: it is either an exponentially growing…
We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called…
When brain signals are recorded in an electroencephalogram or some similar large-scale record of brain activity, oscillatory patterns are typically observed that are thought to reflect the aggregate electrical activity of the underlying…
The Markov-Dyck shifts arise from finite directed graphs. An expression for the zeta function of a Markov-Dyck shift is given. The derivation of this expression is based on a formula in Keller (G. Keller, {\it Circular codes, loop counting,…
Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable…
The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…
Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the…
We apply the theory of height zeta functions to study the asymptotic distribution of rational points of bounded height on projective equivariant compactifications of semi-direct products.
We study the phase synchronization and cluster formation in coupled maps on different networks. We identify two different mechanisms of cluster formation; (a) {\it Self-organized} phase synchronization which leads to clusters with dominant…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…