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We investigate the adaptive Ambush strategy in cyclic models following the rules of the spatial rock-paper-scissors game. In our model, individuals of one species possess cognitive abilities to perceive environmental cues and assess the…
Habitat loss, driven primarily by anthropogenic activity, significantly threatens ecosystem sustainability. While it is well understood that habitat loss is the leading contributor to declines in biodiversity worldwide, the connection…
Pathogen introduction in plant communities can cause serious impact and biodiversity losses that may take long time to manage and restore. Effective control of epidemic spreading in the wild is a problem of paramount importance, because of…
In this paper we consider the Shigesada-Kawasaki-Teramoto (SKT) model to account for stable inhomogeneous steady states exhibiting spatial segregation, which describe a situation of coexistence of two competing species. We provide a deeper…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
A simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary…
We study a chemotaxis-growth system with nonlinear local and nonlocal reactions and gradient-dependent damping. Under suitable conditions on the system parameters and spatial dimension, we prove that solutions exist globally in time and…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
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,…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
This paper is concerned with the spreading speeds of nonlocal dispersal predator-prey systems in shifting habitats under general initial conditions. By employing geometric optics techniques and theory of viscosity solutions, we reformulate…
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…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
Many systems in life sciences have been modeled by reaction-diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events,…
Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic…
Despite extensive progress in characterizing the emergent behavior of active matter, the microscopic origins of self-diffusion in interacting active systems remain poorly understood. Here, we develop a framework that quantitatively links…
The field of active matter explores the behaviors of self propelled agents out of equilibrium, with active suspensions, such as swimming bacteria in solutions, serving as impactful models. These systems exhibit spatio-temporal patterns akin…
This paper presents a homogenisation-based constitutive model to describe the effective tran- sient diffusion behaviour in heterogeneous media in which there is a large contrast between the phase diffusivities. In this case mobile species…
Trajectory prediction is a cornerstone in autonomous driving (AD), playing a critical role in enabling vehicles to navigate safely and efficiently in dynamic environments. To address this task, this paper presents a novel trajectory…
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing…