相关论文: On a phenotype-structured Shigesada--Kawasaki--Ter…
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, we develop a modelling framework for phenotype-structured populations that makes it…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type satisfying the detailed balance condition with the entropy structure of a reversible microscopic…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migration of cell populations driven by this non-local form of…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
Ecological and evolutionary dynamics have been historically regarded as unfolding at broadly separated timescales. However, these two types of processes are nowadays well documented to much more tightly than traditionally assumed,…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion…
Chemotaxis-driven invasions have been proposed across a broad spectrum of biological processes, from cancer to ecology. The influential system of equations introduced by Keller and Segel has proven a popular choice in the modelling of such…
In a previous paper(2021), the author studied the asymptotic behavior of coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. As a result, he proved that…
A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
An implicit Euler finite-volume scheme for an $n$-species population cross-diffusion system of Shigesada--Kawasaki--Teramoto-type in a bounded domain with no-flux boundary conditions is proposed and analyzed. The scheme preserves the formal…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
The rise of trait-based ecology has led to an increased focus on the distribution and dynamics of traits in communities. However, a general theory of trait-based ecology, that can apply across different scales (e.g., species that differ in…
The existence of global nonnegative martingale solutions to a cross-diffusion system of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven. The model describes the segregation dynamics of populations with an arbitrary…
Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
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…