Related papers: On decay-surge population models
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
The symbiotic branching model describes a spatial population consisting of two types that are allowed to migrate in space and branch locally only if both types are present. We continue our investigation of the large scale behaviour of the…
A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
Rate coefficients can fluctuate in statically and dynamically disordered kinetics. Here we relate the rate coefficient for an irreversibly decaying population to the Fisher information. From this relationship we define kinetic versions of…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval,…
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a…
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…
We consider a fully stochastic excitatory neuronal network with a number of subpopulations with different firing rates. We show that as network size goes to infinity, this limits on a deterministic hybrid model whose trajectories are…
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…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…
We study population dynamics through a general growth/degrowth-fragmentation process, with resource consumption and unbounded growth/degrowth, birth and death rates. Our model is structured in a positive trait called energy (which is a…
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population protocol corresponds to a collection of anonymous agents, modeled by…
We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and removed from the system with a uniform…
We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates…
We propose a simple model for sample space reducing (SSR) stochastic process, where the dynamical variable denoting the size of the state space is continuous. In general, one can view the model as a multiplicative stochastic process, with a…