Related papers: Analysis of a chemotaxis system modeling ant forag…
The chemotaxis PDE system with singular sensitivity was originally proposed by Short et al. (Math. Mod. Meth. Appl. Sci., 2008) as the continuum limit of a biased random walk model to account for the formation of crime hotspots and…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
The macroscopic (population-level) dynamics of chemotactic cell movement -- arising from underlying microscopic (individual-based) models -- are often described by parabolic partial differential equations (PDEs) governing the…
We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represended by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows…
We present a model of ant traffic considering individual ants as self-propelled particles undergoing single file motion on a one-dimensional trail. Recent experiments on unidirectional ant traffic in well-formed natural trails showed that…
We propose a mathematical model, namely a reaction-diffusion system, to describe social behaviour of cockroaches. An essential new aspect in our model is that the dispersion behaviour due to overcrowding effect is taken into account {as a…
Mass-conservative reaction-diffusion systems have recently been proposed as a general framework to describe intracellular pattern formation. These systems have been used to model the conformational switching of proteins as they cycle from…
Navigation through narrow passages during colony relocation by the tandem-running ants, $\textit{Diacamma}$ $\textit{indicum}$, is a tour de force of biological traffic coordination. Even on one-lane paths, the ants tactfully manage a…
Ant algorithms are inspired in real ants and the main idea is to create virtual ants that travel into the space of possible solution depositing virtual pheromone proportional to how good a specific solution is. This creates a autocatalytic…
Local interactions, when individuals meet, can regulate collective behavior. In a system without any central control, the rate of interaction may depend simply on how the individuals move around. But interactions could in turn influence…
We investigate the outflux of ions through the channels in a cell membrane. The channels undergo an open/close cycle according to a periodic schedule. Our study is based both on theoretical considerations relying on homogenization theory,…
Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics,…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
We study the adaptive dynamics of predator-prey systems modeled by a dynamical system in which the traits of predators and prey are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
We consider a cross-diffusion system for which the diffusion of each species is governed solely by the aggregate density through a pressure law of logarithmic or fast diffusion type. The model is set over a one dimensional bounded interval,…
This study examines a fully parabolic predator-prey chemo-alarm-taxis system under homogeneous Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ with a smooth boundary $\partial\Omega$. Under specific parameter…
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune system signalling, where infected tissues release chemokines…