相关论文: Synchronization points: growth, asymptotics, congr…

A sofic shift is a shift space consisting of bi-infinite labels of paths from a labelled graph. Being a dynamical system, the distribution of its closed orbits may indicate the complexity of the space. For this purpose, prime orbit and…

Using analytic torsion associated to stable bundles, we introduce zeta functions for compact Riemann surfaces. To justify the well-definedness, we analyze the degenerations of analytic torsions at the boundaries of the moduli spaces, the…

For a bornology $\mathcal{S}$ of subsets of a metric space $(X,d)$, we consider the following unified approaches of hyperspace convergence: convergence induced through uniform convergence of distance functionals…

Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…

In the past few years, the discoveries of small-world and scale-free properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the…

We report experimental studies of synchronization phenomena in a pair of biological neurons that interact through naturally occurring, electrical coupling. When these neurons generate irregular bursts of spikes, the natural coupling…

We investigate networks of automata that synchronise over common action labels. A graph synchronisation topology between the automata is defined in such a way that two automata are connected iff they can synchronise over an action. We show…

Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines,…

Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral…

Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…

This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…

We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…

In this paper we define a symmetric zeta function. We show that it can be analytically continued to a meromorphic function on $\mathbb{C}^3$ with only simple poles at some special hyperplanes. We also calculate the value of a multiple…

We study the efficiency of synchronization in ensembles of identical coupled stochastic oscillator systems. By deriving a chemical Langevin equation, we measure the rate at which the systems synchronize. The rate at which the difference in…

This work has two main purposes. On the one side we investigate in this work a question of H. Esnault on congruence formula in a construction of H. Esnault and C. Xu for the number of rational points on the closed fiber of a singular model…

Synchronized behavior among individuals is a ubiquitous feature of populations. Understanding mechanisms of (de)synchronization demands meaningful, interpretable, computable quantifications of synchrony, relevant to measurements that can be…

Starting from the classical integral representation of the $\zeta(s)$ function introduced by Riemann in 1859, this paper reexamines its analytic symmetry structure. By performing a geometric decomposition of the integral representation, we…

The $L^2$-zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta functions of the finite graphs converge to the $L^2$-zeta…

Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the…