Related papers: Slow-fast systems with stochastic resetting
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
We investigate random searches under stochastic position resetting at rate $r$, in a bounded 1D environment with space-dependent diffusivity $D(x)$. For arbitrary shapes of $D(x)$ and prescriptions of the associated multiplicative…
We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within…
In this work, we study in the framework of the so-called driven tight-binding chain (TBC) the issue of quantum unitary dynamics interspersed at random times with stochastic resets mimicking non-unitary evolution due to interactions with the…
We study a fully-coupled system of conditional slow-fast McKean-Vlasov Stochastic Differential Equations that exhibit full dependence on both the slow and fast components, as well as on the conditional law of the slow component. Our aim is…
We consider a statistical limit of solutions to the compressible Navier--Stokes system in the high Reynolds number regime in a domain exterior to a rigid body. We investigate to what extent this highly turbulent regime can be modeled by an…
For a dynamical system, it is known that the existence of a Lyapunov-type density function, called Lyapunov density or Rantzer's density function, implies convergence of Lebesgue almost all solutions to an equilibrium. Using the duality…
This paper concerns the instantaneous frequency (IF) of continuous-time, zero-mean, complex-valued, proper, mean-square differentiable nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for…
We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error with respect to the small parameter defining the fast time…
In this paper, we study a simple model of a diffusive particle on a line, undergoing a stochastic resetting with rate $r$, via rescaling its current position by a factor $a$, which can be either positive or negative. For $|a|<1$, the…
The effects of Poissonian resetting at a constant rate $r$ on the reaction time between a Brownian particle and a stochastically gated target are studied. The target switches between a reactive state and a non-reactive one. We calculate the…
We study a stochastic differential equation driven by a Poisson point process, which models continuous changes in a population's environment, as well as the stochastic fixation of beneficial mutations that might compensate for this change.…
In this paper, a control scheme for stochastic predefined-time stabilization is proposed, which improves the control effect compared with stochastic finite-time or fixed-time stabilization. The stochastic predefined-time stabilization…
We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches the steady state in an asymptotically exponentially long…
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…
In this work we study the averaging principle for non-autonomous slow-fast systems of stochastic differential equations. In particular in the first part we prove the averaging principle assuming the sublinearity, the Lipschitzianity and the…
The temporal linear stability of plane Poiseuille flow modified by spanwise forcing applied at the walls is considered. The forcing consists of a stationary streamwise distribution of spanwise velocity that generates a steady transversal…
Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…
We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…