Related papers: Invariant measure selection by noise: An Example
We consider a stochastic nonlinear defocusing Schr\"{o}dinger equation with zero-order linear damping, where the stochastic forcing term is given by a combination of a linear multiplicative noise in the Stratonovich form and a nonlinear…
We analyze dynamical systems subjected to an additive noise and their deterministic limit. In this work, we will introduce a notion by which a stochastic system has something like a Markov partition for deterministic systems. For a chosen…
The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the…
It is well known that open dynamical systems can admit an uncountable number of (absolutely continuous) conditionally invariant measures (ACCIMs) for each prescribed escape rate. We propose and illustrate a convex optimisation based…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
We consider the long time statistics of a one-dimensional stochastic Ginzburg-Landau equation with cubic nonlinearity while being subjected to random perturbations via an additive Gaussian noise. Under the assumption that sufficiently many…
We present a class of systems for which the signal-to-noise ratio always increases when increasing the noise and diverges at infinite noise level. This new phenomenon is a direct consequence of the existence of a scaling law for the…
Quantum measurements are crucial to observe the properties of a quantum system, which however unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system while being subject to a…
We provide deterministic controllability conditions that imply exponential mixing properties for randomly forced constrained dynamical systems with possibly unbounded state space. As an application, new ergodicity results are obtained for…
The stochastic quantization of dissipative systems is discussed. It is shown that in order to stochastically quantize a system with dissipation, one has to restrict the Fourier transform of the space-time variable to the positive half…
Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…
There is studied an invariant measure structure of a class of ergodicl discrete dynamical systems by means of the measure generating function method
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a…
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if…
The dynamics of an ensemble of identically prepared two-qubit systems is investigated which is subjected to the iteratively applied measurements and conditional selection of a typical entanglement purification protocol. It is shown that the…
We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…