Related papers: Multiple Patterns Formation for an Aggregation/Dif…
We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their…
We study a predator-prey model with Holling type I functional response, an alternative food source for the predator, and multiple Allee effects on the prey. We show that the model has at most two equilibrium points in the first quadrant,…
Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological…
Typical density functional theory (DFT) and approximations thereto solve the many-electron ground state problem by working from a numerically efficient non-interacting Kohn-Sham reference system; and benefit from useful minimization…
Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of…
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…
We consider the driven dynamics of a probe particle moving through an assembly of particles with competing long-range repulsive and short-range attractive interactions, which form crystal, stripe, labyrinth, and bubble states as the ratio…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
A long-time behavior of solutions to a nonlinear plate model subject to non-conservative and non-dissipative effects and nonlinear damping is considered. The model under study is a prototype for a suspension bridge under the effects of…
One of the aims of systems biology is to build multiple layered and multiple scale models of living systems which can efficiently describe phenomena occurring at various level of resolution. Such models should consist of layers of various…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate-parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
We investigate a nonlocal single-species reaction-diffusion-advection model that integrates the spatial memory of previously visited locations and nonlocal detection in space, resulting in a coupled PDE-ODE system reflective of several…
Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai. The model describes the pressure field thanks to Darcy's type…
We study the existence, regularity and uniqueness for a general class of triangular reaction-cross-diffusion systems coming from the study of starvation driven behavior for two species in competition. This study involves an equivalent…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and…