Related papers: Multi-species Patlak-Keller-Segel system
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
The long time behavior of a model for a first order, weakly reversible chemical reaction network is considered, where the movement of the reacting species is described by kinetic transport. The reactions are triggered by collisions with a…
One of the most important findings in the study of chemotactic process is self-organized cellular aggregation, and a high volume of results are devoted to the analysis of a concentration of single species. Whereas, the multi-species case is…
We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the…
A general class of hybrid models has been introduced recently, gathering the advantages multiscale descriptions. Concerning biological applications, the particular coupled structure fits to collective cell migrations and pattern formation…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
Populations can become spatially organised through chemotaxis autoattraction, wherein population members release their own chemoattractant. Standard models of this process usually assume phenotypic homogeneity, but recent studies have shed…
We consider a family of McKean--Vlasov equations arising as the large particle limit of a system of interacting particles on the positive half-line with common noise and feedback. Such systems are motivated by structural models for systemic…
We investigate collective behavior in a $Q$-species Vicsek model with a nonreciprocal velocity alignment interaction. This system is characterized by a constant phase shift $\alpha$ in the inter-species velocity alignment rule. While the…
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero.…
In this paper we consider a microscopic model of a simple ecosystem. The basic ingredients of this model are individuals, and both the phenotypic and genotypic levels are taken in account. The model is based on a long range cellular…
A finite volume scheme for the (Patlak-) Keller-Segel model in two space dimensions with an additional cross-diffusion term in the elliptic equation for the chemical signal is analyzed. The main feature of the model is that there exists a…
Collective dynamics can be observed among many animal species, and have given rise in the last decades to an active and interdisciplinary field of study. Such behaviors are often modeled by active matter, in which each individual is…
In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…
The theoretical understanding of pattern formation in active systems remains a central problem of interest. Heterogeneous flocks made up of multiple species can exhibit a remarkable diversity of collective states that cannot be obtained…
We consider a generalised Keller-Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are more singular than Newtonian interaction. We show uniqueness of…
Many-body stochastic processes with weighted multiplicative interactions are investigated analytically and numerically. An interaction rate between particles with quantities $x, y$ is controlled by a homogeneous symmetric kernel $K(x, y)…
We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type…
Test particles interact with a medium by means of a bimolecular reversible chemical reaction. Two species are assumed to be much more numerous so that they are distributed according fixed distributions: Maxwellians and Dirac's deltas.…
We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and…