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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 investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints.…
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…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
We construct a data-driven model of flows in graphs that captures the essential elements of the movement of workers between jobs in the companies (firms) of entire economic systems such as countries. The model is based on the observation…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
The dynamical properties of road traffic time series from North-Rhine Westphalian motorways are investigated. The article shows that road traffic dynamics is well described as a persistent stochastic process with two fixed points…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
In the paper we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a viscous gas. We use the model of a harmonic polyatomic (more…
We study the dynamics of condensation in a misanthrope process with nonlinear jump rates and factorized stationary states. For large enough density, it is known that such models have a phase separated state, with a non-zero fraction of the…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous nonequilibrium phase transition from a condensed phase, in which a single `flock'…
A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes where they receive service according to the Processor-Sharing policy. Once their service requirement is…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
This article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically time-dependent transition rates that satisfy the detailed balance condition at any time. We show that under general…
Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model…