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The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For…
Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information…
In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics. We consider deterministic (i.e., a priori averaged) and…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
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'…
Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that…
In this work, we consider a differential description of the evolution of the state of a reaction-diffusion system under environmental fluctuations. We are interested in estimating the state of the system when only partial observations are…
We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
Turbulent reacting flows confined to ducts are plagued by thermoacoustic instability, a state in which a positive feedback between flow, flame and acoustic perturbations leads to the emergence of catastrophically high-amplitude oscillatory…
We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion equation posed on the bounding unit sphere through a linear…
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
We present a simple analytical tool which gives an approximate insight into the stationary behavior of nonlinear systems undergoing the influence of a weak and rapid noise from one dominating source, e.g. the kinetic equations describing a…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…
Bursting is a periodic transition between a quiescent state and a state of repetitive spiking. The phenomenon is ubiquitous in a variety of neurophysical systems. We numerically study the dynamical properties of a normal form of subcritical…
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…