Related papers: Pattern formation within phenotype-structured chem…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
The Keller-Segel (KS) chemotaxis system is used to describe the overall behavior of a collection of cells under the influence of chemotaxis. However, solving the KS chemotaxis system and generating its aggregation patterns remain…
Many living and non-living complex systems can be modeled and understood as collective systems made of heterogeneous components that self-organize and generate nontrivial morphological structures and behaviors. This chapter presents a brief…
We consider a population structured by a spacevariable and a phenotypical trait, submitted to dispersion,mutations, growth and nonlocal competition. This population is facing an {\it environmental gradient}: to survive at location $x$, an…
In this paper we study a class of stochastic individual-based models that describe the evolution of haploid populations where each individual is characterised by a phenotype and a genotype. The phenotype of an individual determines its…
Quantitatively predicting phenotype variables by the expression changes in a set of candidate genes is of great interest in molecular biology but it is also a challenging task for several reasons. First, the collected biological…
We study a size-structured population model in which individual cells grow at a rate determined by a fluctuating internal variable (e.g., gene expression levels). Many previous models of phenotypically heterogeneous populations can be…
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…
Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections…
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…
We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…
We investigate an interacting particle model to simulate a foraging colony of ants, where each ant is represented as an active Brownian particle. The interactions among ants are mediated through chemotaxis, aligning their orientations with…
A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a…
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
One of the fundamental principles driving diversity or homogeneity in domains such as cultural differentiation, political affiliation, and product adoption is the tension between two forces: influence (the tendency of people to become…
The purpose of this work is the study of \textit{chemotaxis} and how to model it through the equations of Keller-Segel. \textit{Chemotaxis} is a natural process which induces the organisms to direct their movement according to certain…
Chemotaxis phenomena govern the directed movement of micro-organisms in response to chemical stimuli. In this paper, we investigate two Keller--Segel systems of reaction-advection-diffusion equations modeling chemotaxis on thin networks.…
Most of the DNA that composes a complex organism is non-coding and defined as junk. Even the coding part is composed of genes that affect the phenotype differently. Therefore, a random mutation has an effect on the specimen fitness that…
Models of the consensus of the individual state in social systems have been the subject of recent researches in the physics literature. We investigate how network structures coevolve with the individual state under the framework of social…
Predicting fitness of biologically-active populations, communities or systems in fluctuating environments is a long-standing challenge. Phenotypic plasticity and bet-hedging strategy, two key evolutionary traits living systems harness to…