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The appearance of topological effects in systems exhibiting a non-trivial topological band structure strongly relies on the coherent wave nature of the equations of motion. Here, we reveal topological dynamics in a classical stochastic…
Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined…
We consider the dynamics of a 1D system evolving according to a deterministic drift and randomly forced by two types of jumps processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously…
The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…
This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.
We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium…
Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…
We consider random walks in i.i.d. elliptic random environments which are not uniformly elliptic. We introduce a computable condition in dimension $d=2$ and a general condition valid for dimensions $d\ge 2$ expressed in terms of the exit…
This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
There is a wide variety of data mining methods available, and it is generally useful in exploratory data analysis to use many different methods for the same dataset. This, however, leads to the problem of whether the results found by one…
We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
A random walk generated by a sum of independent identity distributed random variables with positive expectation is considered. The limiting distributions for the first- passage -time of a step-function boundary are derived.
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…
In physics, it is frequently needed to precisely measure the count rate of some process. Quite often one needs to account for electronics dead time, pile-up and other features of data acquisition system to avoid systematic shifts of the…
By the methods of multitype branching processes in random environment counted by random characteristics we study the tail distribution of busy periods and some other characteristics of the branching type polling systems in which the service…
The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…
We demonstrate the advantages of randomization in coherent quantum dynamical control. For systems which are either time-varying or require decoupling cycles involving a large number of operations, we find that simple randomized protocols…