Related papers: Multi-species Patlak-Keller-Segel system
Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely…
In this work, we study a stochastic system of N particles associated with the parabolic-parabolic Keller-Segel system. This particle system is singular and non Markovian in that its drift term depends on the past of the particles. When the…
This paper is concerned with global solvability of a fully parabolic system of Keller--Segel-type involving non-monotonic signal-dependent motility. First, we prove global existence of classical solutions to our problem with generic…
Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped 2-d system of particles interacting by repulsive forces. As a…
We investigate how the pattern of contacts between species in mutualistic ecosystems is affected by the phylogenetic proximity between the species of each guild. We develop several theoretical tools to measure that effect and we use them to…
This review is dedicated to recent results on the 2d parabolic-elliptic Patlak-Keller-Segel model, and on its variant in higher dimensions where the diffusion is of critical porous medium type. Both of these models have a critical mass…
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered…
A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we present a solvable example of such a feedback mechanism in…
We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions…
An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…
This paper is devoted to the analysis of the classical Keller-Segel system over $\mathbb{R}^d$, $d\geq 3$. We describe as much as possible the dynamics of the system characterized by various criteria, both in the parabolic-elliptic case and…
As it is well known, the parabolic-elliptic Keller-Segel system of chemotaxis on the plane has global-in-time regular nonnegative solutions with total mass below the critical value $8\pi$. Solutions with mass above $8\pi$ blow up in a…
Systems of active particles can show a large variety of collective behavior. In theory, two aspects determine the collective behavior: the model at the particle level and the parameter regime. While many studies consider a single model and…
The recent realization that entire communities fuse and separate (community coalescence) has led to a reappraisal of the forces determining species diversity and dynamics, especially in microbial communities where coalescence is likely…
We introduce stochastic models of chemotaxis generalizing the deterministic Keller-Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean's…
We investigate the replicator dynamics with "sparse" symmetric interactions which represent specialist-specialist interactions in ecological communities. By considering a large self interaction $u$, we conduct a perturbative expansion which…
Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…
Particles that are catalytically-active and chemotactic can interact through the concentration fields upon which they act, which in turn may lead to wide-scale spatial self-organization. When these active particles interact through several…
We consider the problem of understanding the coordinated movements of biological or artificial swarms. In this regard, we propose a learning scheme to estimate the coordination laws of the interacting agents from observations of the swarm's…
It is known that, for the parabolic-elliptic Keller-Segel system with critical porous-medium diffusion in dimension $\RR^d$, $d \ge 3$ (also referred to as the quasilinear Smoluchowski-Poisson equation), there is a critical value of the…