Related papers: Dynamical Effects of Multiplicative Feedback on a …
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…
In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of…
In this paper, we study the contractivity of nonlinear stochastic differential equations (SDEs) driven by deterministic inputs and Brownian motions. Given a weighted $\ell_2$-norm for the state space, we show that an SDE is incrementally…
We study the role of multiplicative colored noise for different values of the correlation time $\tau_c$ in the dynamics of two competing species, described by generalized Lotka-Volterra equations. The multiplicative colored noise models the…
Unidirectionally coupled dynamical system is studied by focusing on the input (or boundary) dependence. Due to convective instability, noise at an up-flow is spatially amplified to form an oscillation. The response, given by the down-flow…
A parabolic stochastic PDE is studied analytically and numerically, when a bifurcation parameter is slowly increased through its critical value. The aim is to understand the effect of noise on delayed bifurcations in systems with spatial…
The classification of the long-term behavior of dynamical systems is a fundamental problem in mathematics. For both deterministic and stochastic dynamics specific classes of models verify Palis' conjecture: the long-term behavior is…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with…
Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values.…
The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme…
Research on stochastic differential equations (SDE) involving both additive and multiplicative noise has been extensive. In situations where the primary process is driven by a multiplicative stochastic process, additive white noise…
Due to inherent noise in intracellular networks cellular decisions can be random, so genetically identical cells can display different phenotypic behavior even in identical environments. Most previous work in understanding the…
Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…
We study the interplay between noise and a positive feedback mechanism in an excitable system that generates events. We show that such a system can exhibit a bistability in the dynamics of the event generation (states of low and high…
"Noise-induced volatility" refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to…