Related papers: Random dynamical systems on a real line

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the…

We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…

In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

In this work, we investigate scale invariance in the temporal evolution and chaotic regime of discrete dynamical systems. By exploiting the close interrelation between scaling and inversion transformations, we formulate scale symmetry in…

We study a rolling model from the perspective of probability. More precisely, we consider a Riemannian manifold rolling against Euclidean space, where the rolling is coupled with random slipping and twisting. The system is modelled by a…

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…

We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…

Networks have been studied mainly using statistical methods. Here I collect some dynamical systems tools which are useful to study both the dynamics on networks and their evolution. They include decomposition of differential dynamics,…

Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space…

This is the second part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. The current part focuses on applications of general…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

Reactivity, contractivity, and Lyapunov exponents are powerful tools for studying the stability properties of dynamical systems and have been extensively investigated in the literature for decades. In this paper, we review and extend the…

We adjust the classical random waypoint mobility model used in the study of telecommunication networks to a more realistic setting by allowing participants of the network to return to popular places and individual homes. We show that the…

We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…

Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…

Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…