Related papers: Linear stochastic dynamics with nonlinear fractal …

The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of…

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…

Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…

The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…

We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a…

We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on…

Control of linear dynamics with multiplicative noise naturally introduces robustness against dynamical uncertainty. Moreover, many physical systems are subject to multiplicative disturbances. In this work we show how these dynamics can be…

We introduce a new class of models in which a large number of "agents" organize under the influence of an externally imposed coherent noise. The model shows reorganization events whose size distribution closely follows a power law over many…

Contemporary technological challenges often involve many degrees of freedom in a distributed or networked setting. Three aspects are notable: the variables are usually associated with the nodes of a graph with limited communication…

A two dimensional flow model is introduced with deterministic behavior consisting of bursts which become successively larger, with longer interburst time intervals between them. The system is symmetric in one variable x and there are bursts…

In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…

Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…

We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…

We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…

This work considers state dynamics driven by Periodic Autoregressive Moving Average noise, and control of the system over time. Such processes appear frequently in applications involving the environment, such as energy and agriculture.…

We study the stationary probability distribution of a system driven by shot noise. We find that, both in the overdamped and underdamped regime, the coordinate distribution displays power-law singularities in its central part. For…

Neuronal networks can generate burst events. It remains unclear how to analyse interburst periods and their statistics. We study here the phase-space of a mean-field model, based on synaptic short-term changes, that exhibit burst and…

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…