Related papers: Stability of non-conservative cross diffusion mode…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
In this paper, we investigate a generalised model of $N$ particles undergoing second-order non-local interactions on a lattice. Our results have applications across many research areas, including the modelling of migration, information…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
We present a novel study on enhancing the capability of preserving the content in world models, focusing on a property we term World Stability. Recent diffusion-based generative models have advanced the synthesis of immersive and realistic…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…
In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown,…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends results of the…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
Certain types of active systems can be treated as an equilibrium system with excess non-conservative forces driving some of the microscopic degrees of freedom. We derive results for how many particles interacting with each other with both…