Related papers: Synchronization rates and limit laws for random dy…
We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis,…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
We study contraction conditions for an iterated function system of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space,…
We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate…
We extend the spectral method for proving limit theorems to random non-uniformly expanding dynamical systems. This yields the CLT and moderate deviations principles (MDP). We show that as the amount of non-uniformity decreases the CLT rates…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared.…
In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
In order to give quantitative estimates for approximating the ergodic limit, we investigate probabilistic limit behaviors of time-averaging estimators of numerical discretizations for a class of time-homogeneous Markov processes, by…
We study the dynamics of condensation of the inclusion process on a one-dimensional periodic lattice in the thermodynamic limit, generalising recent results on finite lattices for symmetric dynamics. Our main focus is on totally asymmetric…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown…
We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbour coupling never allows spatiotemporal synchronization in our…
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…
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…
Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic…
We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…