Related papers: Steady State Of Random Dynamical Systems
In this paper we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting,…
We study nonautonomous discrete dynamical systems with randomly perturbed trajectories. We suppose that such a system is generated by a sequence of continuous maps which converges uniformly to a map $f$. We give conditions, under which a…
A simple weakly frequency dependent model for the dynamics of a population with a finite number of types is proposed, based upon an advantage of being rare. In the infinite population limit, this model gives rise to a non-smooth dynamical…
We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a H\"older space which is separable.
This paper presents an analysis approach to finite-time attraction in probability concerns with nonlinear systems described by nonlinear random differential equations (RDE). RDE provide meticulous physical interpreted models for some…
We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
We consider a problem of placing generators of rewards to be collected by randomly moving agents in a network. In many settings, the precise mobility pattern may be one of several possible, based on parameters outside our control, such as…
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…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the…
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…
We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random…
The important phenomenon of "stickiness" of chaotic orbits in low dimensional dynamical systems has been investigated for several decades, in view of its applications to various areas of physics, such as classical and statistical mechanics,…