Related papers: A meeting point of entropy and bifurcations in cro…
We study a fractional cross-diffusion system that describes the evolution of multi-species populations in the regime of large-distance interactions in a bounded domain. We prove existence and weak-strong uniqueness results for the…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
In this paper, we consider a continuous-time model with discrete and dis-tributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
We investigate an epidemiological model that incorporates waning of immunity at the individual level and boosting of the immune system upon re-exposure to the pathogen. When immunity is fully restored upon boosting, the system can be…
Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the…
The dryland vegetation model proposed by Rietkerk and collaborators has been explored from a bifurcation perspective in several previous studies. Our aim here is to explore in some detail the bifurcation phenomena present when the…
We performed a thorough sensitivity analysis of the herd immunity threshold for discrete-time SIR compartmental models with a static network structure. We find unexpectedly that these models violate classical intuition which holds that the…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing…
Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a…
Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that…
Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend…