相关论文: Topological synchronisation or a simple attractor?

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…

Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the…

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…

Topological surgery occurs in natural phenomena where two points are selected and attracting or repelling forces are applied. The two points are connected via an invisible `thread'. In order to model topologically such phenomena we…

We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…

We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.

Existence of different kinds of synchronizations, namely anticipatory, complete and lag type synchronizations (both exact and approximate), are shown to be possible in time-delay coupled piecewise linear systems. We deduce stability…

Through numerical simulations we analyze the synchronization time and the Lyapunov dimension of a coupled map lattice consisting of a chain of chaotic logistic maps exhibiting power law interactions. From the observed behaviors we find a…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…

Recent years have witnessed a surge of interest in performing measurements within topological phases of matter, e.g., symmetry-protected topological (SPT) phases and topological orders. Notably, measurements of certain SPT states have been…

We study the problem of synchronizing a general complex network by means of an adaptive strategy in the case where the network topology is slowly time varying and every node receives at each time only one aggregate signal from the set of…

We formulate both Markov chain Monte Carlo (MCMC) sampling algorithms and basic statistical physics in terms of elementary symmetries. This perspective on sampling yields derivations of well-known MCMC algorithms and a new parallel…

Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough…

We study a family of dynamical systems obtained by coupling an Anosov map on the two-dimensional torus -- the chaotic system -- with the identity map on the one-dimensional torus -- the neutral system -- through a dissipative interaction.…

This research investigates the intricate domain of synchronization problem among multiple agents operating within a dynamic fast switching network topology. We concentrate on cluster synchronization within coupled linear system under…

Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several…

We rigorously show that dissipatively driven Frenkel-Kontorova models with either uniform or time-periodic driving asymptotically synchronize for a wide range of initial conditions. The main tool is a new Lyapunov function, as well as a 2D…