Related papers: Topological synchronisation or a simple attractor?
This paper investigates the dynamical system governing the phase differences between three identical oscillators arranged symmetrically and coupled by burst interactions. By constructing a discrete Lyapunov function, we prove the existence…
For a smooth Morse-Smale vector field with Lyapunov constraints (Lyapunov function) one shows how and why the non-triviality of the cohomology, as concluded from its additive structure, detects rest points and the multiplicative structure…
The notion of an attractor has various definitions in the theory of dynamical systems. Under compactness assumptions, several of those definitions coincide and the theory is rather complete. However, without compactness, the picture becomes…
Measure synchronization is a well-known phenomenon in coupled classical Hamiltonian systems over last two decades. In this paper, synchronization for coupled Harper system is investigated in both classical and quantum contexts. The concept…
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…
For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov…
A one-parameter family of time-reversible systems on $\mathbb{T}^3$ is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
We study some topological properties of attractors.
For topologically mixing locally conformal semigroup actions generated by a finite collection of $C^{1+\alpha}$ conformal local diffeomorphisms, we provide a countable Markov partition satisfying the finite images and the finite cycle…
Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…
We study asymptotic synchronization at the level of global attractors in a class of coupled second order in time models which arises in dissipative wave and elastic structure dynamics. Under some conditions we prove that this…
We study synchronization of low-dimensional ($d=2,3,4$) chaotic piecewise linear maps. For Bernoulli maps we find Lyapunov exponents and locate the synchronization transition, that numerically is found to be discontinuous (despite…
In the context of stationary $\mathbb{Z}^d$ nearest-neighbour Gibbs measures $\mu$ satisfying strong spatial mixing, we present a new combinatorial condition (the topological strong spatial mixing property (TSSM)) on the support of $\mu$…
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…
Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the transient…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
The existence of a global attractor is proved for the skew-product semiflow induced by almost periodic Nicholson systems and new conditions are given for the existence of a unique almost periodic positive solution which exponentially…