Related papers: A note on the topological synchronisation of unimo…
In this paper, we study Markovian random iterations of maps on standard measurable spaces. We establish a one-to-one correspondence between stationary measures and a certain class of invariant measures of a Markovian random iteration,…
The stability analysis of synchronization in time-varying higher-order networked structures (simplicial complexes) is one of the challenging problem due to the presence of time-varying group interactions. In this context, most of the…
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…
We study Markov multi-maps of the interval from the point of view of topological dynamics. Specifically, we investigate whether they have various properties, including topological transitivity, topological mixing, dense periodic points, and…
Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has lead to the generation of some coupled chaotic maps with an invariant measure. It is shown that these…
We study one-dimensional lattice systems with pair-wise interactions of infinite range. We show projective convergence of Markov measures to the unique equilibrium state. For this purpose we impose a slightly stronger condition than…
We study the pointwise perturbations of countable Markov maps with infinitely many inverse branches and establish the following continuity theorem: Let $T_k$ and $T$ be expanding countable Markov maps such that the inverse branches of $T_k$…
In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature, sync function Lipschitz…
In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually…
We consider weak invariance principles (functional limit theorems) in the domain of a stable law. A general result is obtained on lifting such limit laws from an induced dynamical system to the original system. An important class of…
In presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one…
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.…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
We study the convergence properties of a collapsed Gibbs sampler for Bayesian vector autoregressions with predictors, or exogenous variables. The Markov chain generated by our algorithm is shown to be geometrically ergodic regardless of…
In $4$-dimensional pure compact $U(1)$ lattice gauge theory, we analyse topological aspects of the dynamics of monopoles across the deconfinement phase transition. We do this using tools from Topological Data Analysis (TDA). We demonstrate…
Time series datasets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the…
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
We analyze a distributed algorithm for estimation of scalar parameters belonging to nodes in a mobile network from noisy relative measurements. The motivation comes from the problem of clock skew and offset estimation for the purpose of…
A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature,…