Related papers: Linear stochastic dynamics with nonlinear fractal …
We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…
Utilization of noise for the control of a class of non-linear systems is presented. The application of state-multiplicative noise as a mean of control is far more limited then the use of standard determinis?tic gains. Nevertheless, so…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
In this manuscript we analyse the long-term probability density function of non-stationary dynamical processes which are enclosed inward the Feller class of processes with time varying exponents for multiplicative noise. The update in the…
Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order structural (height-height correlation)…
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
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…
Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…
We consider a dynamical system which has a stable attractor and which is perturbed by an additive noise. Under some quite typical conditions, the fluctuations from the attractor are intermittent and have a probability distribution with…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…