Related papers: On the influence of cross-diffusion in pattern for…
We introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual…
We consider a periodic reaction diffusion system which, because of competition between $u$ and $v$, does not enjoy the comparison principle. It also takes into account mutations, allowing $u$ to switch to $v$ and vice versa. Such a system…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
We perform a bifurcation analysis on an SIR model involving two pathogens that influences each other. Partial cross-immunity is assumed and coinfection is thought to be less transmittable then each of the diseases alone. The susceptible…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…
We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each $N\in\mathbb{N}$, such $T$-periodic traveling waves are easily seen to be nonlinearly asymptotically stable…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
In this paper, we study the large time behaviour of solutions of multistable reaction-diffusion equations in $\mathbb{R}^N$, with a spatially periodic heterogeneity. By multistable, we mean that the problem admits a finite -- but…
This work introduces a new class of cross-diffusion systems for studying overcrowding dispersal of two species. The approach, based on proximal minimization energy through a minimum flow process, offers a potential generalization of…
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…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…
An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence…
We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter…
The short-time and long-time dynamics of the Bak-Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibits an initial…