Related papers: Hill's Equation with Small Fluctuations: Cycle to …
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
Building upon the eco-evolutionary game dynamics framework established by Tilman et al., we investigate stochastic fluctuations in a two-strategy system incorporating environmental feedback mechanisms, where the payoff matrix exhibits…
In this paper we investigate the normal and the large fluctuations of additive functionals associated with a stochastic process under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very…
We study the asymptotics for the lengths $L_N(q)$ of the instability tongues of Hill equations that arise as iso-energetic linearization of two coupled oscillators around a single-mode periodic orbit. We show that for small energies, i.e.…
We propose a mechanism to produce fluctuations in the viscosity parameter ($\alpha$) in differetially rotating discs. We carried out a nonlinear analysis of a general accretion flow, where any perturbation on the background $\alpha$ was…
We experimentally study the fluctuations of the work done by an external Gaussian random force on two different stochastic systems coupled to a thermal bath: a colloidal particle in an optical trap and an atomic force microscopy cantilever.…
In this paper we apply the method of stochastic characteristics to a Lighthill-Whitham-Richards model. The stochastic perturbation can be seen as errors in measurement of the traffic density. For concrete examples we solve the equation…
We show that in a broad class of processes that show a $1/f^{\alpha}$ spectrum, the power also explicitly depends on the characteristic time scale. Despite an enormous amount of work, this generic behavior remains so far overlooked and…
This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel is summable and ascribe growth bounds to the exogenous…
A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…
We consider a stochastic logistic growth model involving both birth and death rates in the drift and diffusion coefficients for which extinction eventually occurs almost surely. The associated complete Fokker-Planck equation describing the…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
In this work, we present and analyze a system of PDEs, which models tumor growth by considering chemotaxis, active transport, and random effects. The stochasticity of the system is modelled by random initial data and Wiener noises that…
We investigate the non-equilibrium dynamics of isolated quantum spin systems via an exact mapping to classical stochastic differential equations. We show that one can address significantly larger system sizes than recently obtained,…
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws…
Laboratory earthquakes exhibit characteristics of a low dimensional random attractor with a dimension similar to that of natural slow earthquakes. A model of stochastic differential equations based on rate and state-dependent friction…
The quantum hydrodynamic analogy (QHA) equivalent to the Schrodinger equation is generalized to its stochastic version by a systematic technique. On large scale, the quantum stochastic hydrodynamic analogy (QSHA) shows dynamics that under…
We use the optimal fluctuation method to evaluate the short-time probability distribution $\mathcal{P}\left(H,L,t\right)$ of height at a single point, $H=h\left(x=0,t\right)$, of the evolving Kardar-Parisi-Zhang (KPZ) interface…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially…