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A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…
We quantify the effect of Gaussian white noise on fast--slow dynamical systems with one fast and two slow variables, which display mixed-mode oscillations owing to the presence of a folded-node singularity. The stochastic system can be…
This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…
The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic…
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…
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…
Noise induced changes in the critical and oscillatory behavior of a Prey-Predator system are studied using power spectrum density and Spectral Amplification Factor (SAF) analysis. In the absence of external noise, the population densities…
The impact of environmental fluctuation on species diversity is studied with a model of the evolutionary ecology of microorganisms. We show that environmental fluctuation induces evolutionary branching and assures the consequential…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…
Systems in nature are stochastic as well as nonlinear. In traditional applications, engineered filters aim to minimize the stochastic effects caused by process and measurement noise. Conversely, a previous study showed that the process…
We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of…
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system,…
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense…
We present a new stochastic model, based on a 0-dimensional version of the well known biogeochemical flux model (BFM), which allows to take into account the temperature random fluctuations present in natural systems and therefore to…
Stochastic resetting and noise-enhanced stability are two phenomena which can affect the lifetime and relaxation of nonequilibrium states. They can be considered as measures of controlling the efficiency of the completion process when a…