相关论文: Stochastic patterns in a 1D Rock-Paper-Scissor mod…
We study the phenomenon of cyclic dominance in the paradigmatic Rock--Paper--Scissors model, as occurring in both stochastic individual-based models of finite populations and in the deterministic replicator equations. The mean-field…
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…
Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…
The cooperative binding of molecular agents onto a substrate is pervasive in living systems. To study whether a system shows cooperativity, one can rely on a fluctuation analysis of quantities such as the number of substrate-bound units and…
In a previous work, we presented a model that integrates cancer cell differentiation and immunotherapy, analysing a particular therapy against cancer stem cells by cytotoxic cell vaccines. As every biological system is exposed to random…
We study competition of two non-motile bacterial strains in a three-dimensional channel numerically, and analyze how their configuration evolves in space and time. We construct a lattice model that takes into account self-replication,…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
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…
We examine a biomolecular machine involving a driven, observable process coupled to a hidden process in a kinetically cooperative manner. A stochastic thermodynamics framework is employed to analyze a fluctuation theorem for the…
Clonal interference, competition between multiple co-occurring beneficial mutations, has a major role in adaptation of asexual populations. We provide a simple individual based stochastic model of clonal interference taking into account a…
We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three…
Stochastic models for pore collapse in granular materials are developed. First, a general fluctuating stress-strain relation for a plastic flow rule is derived. The fluctuations account for non-associativity in plastic deformations…
In the present paper we propose an improvement of the Gillespie algorithm allowing us to study the time evolution of an ensemble of chemical reactions occurring in a varying volume, whose growth is directly related to the amount of some…
The evolution and emergence of antibiotic resistance is a major public health concern. The understanding of the within-host microbial dynamics combining mutational processes, horizontal gene transfer and resource consumption, is one of the…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
Laboratory experiments with bacterial colonies, under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such…
Investigation of protein self-assembly processes is important for the understanding of the growth processes of functional proteins as well as disease-causing amyloids. Inside cells, intrinsic molecular fluctuations are so high that they…
We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…