Related papers: A stochastic analysis of the spatially extended Ma…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
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…
We study the Swift-Hohenberg equation - a paradigm model for pattern formation - with "large" spatially periodic coefficients and find a Turing bifurcation that generates patterns whose leading order form is a Bloch wave modulated by…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
The Boltzmann kinetic equation is obtained from an integro-differential master equation that describes a stochastic dynamics in phase space of an isolated thermodynamic system. The stochastic evolution yields a generation of entropy,…
A systematic analysis of the Eckhaus instability in the one-dimensional Ginzburg-Landau equation is presented. The analysis is based on numerical integration of the equation in a large (xt)-domain. The initial conditions correspond to a…
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium…
Over the last few decades, ecologists have come to appreciate that key ecological patterns, which describe ecological communities at relatively large spatial scales, are not only scale dependent, but also intimately intertwined. The…
Recent work on the behaviour of localised states in pattern forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result of its simplicity, has additional structure --- it is…
The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based…
Traditional population models that include predator-prey interactions attribute demographic changes directly to predation-related effects. However, predator-induced fear in prey has increasingly been recognised as an important factor…
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the…
We discuss general multi-dimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety…
The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatial nonhomogeneous periodic solutions, which is induced by nonlocal…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
The influence of an external random field on the competition process in a nonlinear open spatially extended system is analyzed numerically. A three-component model is chosen as the competition model in which a "weak" species can move in…
This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…