相关论文: Synchronization points: growth, asymptotics, congr…
We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type…
We study how a coupled array of spiking chaotic systems synchronizes to an external driving in a short time. Synchronization means spike separation at adjacent sites much shorter than the average inter-spike interval; a local lack of…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
Synchronization plays a fundamental role in healthy cognitive and motor function. However, how synchronization depends on the interplay between local dynamics, coupling and topology and how prone to synchronization a network with given…
The topological zeta function of a matroid is a rational function as well as a valuative invariant of the matroid, encoding rich combinatorial information. We analyze topological zeta functions of matroids from the vantage point of several…
Synchronization resulting in unified collective behavior of the individual elements of a system that are weakly coupled to each other has long fascinated scientists. Examples range from the periodic oscillation of coupled pendulum clocks to…
The problem of synchronization of coupled Hamiltonian systems exhibits interesting features due to the non-uniform or mixed nature (regular and chaotic) of the phase space. We study these features by investigating the synchronization of…
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 show that the unavoidable increase in neuronal response latency to ongoing stimulation serves as a nonuniform gradual stretching of neuronal circuit delay loops and emerges as an essential mechanism in the formation of various types of…
We give a definition of convergence of differential of Lipschitz functions with respect to measured Gromov-Hausdorff topology. As their applications, we give a characterization of harmonic functions with polynomial growth on asymptotic…
The problem of synchronization over a group $\mathcal{G}$ aims to estimate a collection of group elements $G^*_1, \dots, G^*_n \in \mathcal{G}$ based on noisy observations of a subset of all pairwise ratios of the form $G^*_i {G^*_j}^{-1}$.…
We show that generating functions associated to the sequence of convergents of a quadratic irrational are related in a natural way to the dynam- ical zeta function of a hyperbolic automorphism of the 2-torus. As a corollary, this shows that…
Group contraction is an algebraic map that relates two classes of Lie groups by a limiting process. We utilize this notion for the compactification of the class of Cartan motion groups. The compactification process is then applied to reduce…
In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…
The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was…
The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped…
We graft synchronization onto Girard's Geometry of Interaction in its most concrete form, namely token machines. This is realized by introducing proof-nets for SMLL, an extension of multiplicative linear logic with a specific construct…
We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based…
Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization…