Related papers: Asymptotics for a class of iterated random cubic o…

The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a…

We provide a unified analytic approach to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and random attractors. Part I deals with driving paths of finite…

For uniform random permutations conditioned to have no long cycles, we prove that the total number of cycles satisfies a central limit theorem. Under additional assumptions on the asymptotic behavior of the set of allowed cycle lengths, we…

We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing…

In this paper, a proof of asymptotic stability for the combined system-optimizer dynamics associated with a class of real-time methods for equality constrained nonlinear model predictive control is presented. General Q-linearly convergent…

We analyze the dynamics of a system qubit interacting by means a sequence of pairwise collisions with an environment consisting of just two qubits. We show that the density operator of the qubits approaches a common time averaged…

A microscopic model is developed, within the frame of the theory of quantitative traits, to study both numerically and analytically the combined effect of competition and assortativity on the sympatric speciation process, i.e. speciation in…

We apply the dynamical systems tools to study the asymptotic properties of a cosmological model based on a non-linear modification of General Relativity in which the standard Einstein-Hilbert action is replaced by one of Dirac-Born-Infeld…

The composite systems can be non-uniquely decomposed into parts (subsystems). Not all decompositions (structures) of a composite system are equally physically relevant. In this paper we answer on theoretical ground why it may be so. We…

In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various…

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…

In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…

In this short note we study a dynamical system generated by a two-parametric quadratic operator mapping 3-dimensional simplex to itself. This is an evolution operator of the frequencies of gametes in a two-locus system. We find the set of…

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…

We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that…

We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…

It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…

A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random…

Properties of systems with majority voting rules have been exhaustingly studied. In this work we focus on the randomized case - where the system is initialized by randomized initial set of seeds. Our main aim is to give an asymptotic…

We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…