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A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…
Natural flocks (aligned) and swarms (non-aligned) both exhibit features of near-criticality, challenging their treatment as two ends of the same phase transition. We present a model for the aggregation of active individuals, in which their…
We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modelling. In the asymptotic regime of slow diffusion, that coincides…
Recent investigations have provided important insights into the complex structure and dynamics of collectively moving flocks of living organisms. Two intriguing observations are, scale-free correlations in the velocity fluctuations, in the…
We investigate the system of two coupled one-dimensional Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equations which possess the global conservation law. Such system of equations has been recently derived for the quasiparticle densities in…
Internal feedbacks are commonly present in biological populations and can play a crucial role in the emergence of collective behavior. We consider a generalization of Fisher-KPP equation to describe the temporal evolution of the…
This work investigates a model describing the interaction of two species in habiting separate but adjacent areas. These populations are governed by a system of equations that account for spatial variations in growth rates and the effects of…
How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a…
We study the role of demographic fluctuations in typical endemics as exemplified by the stochastic SIRS model. The birth-death master equation of the model is simulated using exact numerics and analysed within the linear noise…
Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
The growth of complex populations, such as microbial communities, forests, and cities, occurs over vastly different spatial and temporal scales. Although research in different fields has developed detailed, system-specific models to…
We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc.\ Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed population of two…
Motivated by the ubiquity of turbulent flows in realistic conditions, effects of turbulent advection on two models of classical non-linear systems are investigated. In particular, we analyze model A (according to the Hohenberg-Halperin…
We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…