Related papers: Solutions with a bounded support promote permanenc…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
This paper is concerned with the death-birth updating process. This model is an example of a spatial game in which players located on the~$d$-dimensional integer lattice are characterized by one of two possible strategies and update their…
Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
Recent contributions address the problem of language coexistence as that of two species competing to aggregate speakers, thus focusing on the dynamics of linguistic traits across populations. They draw inspiration from physics and biology…
Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells interacting with a chemoattractant and a nutrient. The…
In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for studying more complex non-transitive…
Natural selection favors the more successful individuals. This is the elementary premise that pervades common models of evolution. Under extreme conditions, however, the process may no longer be probabilistic. Those that meet certain…
In this work, we analyse the relationship between heterogeneity and cooperation. Previous investigations suggest that this relation is nontrivial, as some authors found that heterogeneity sustains cooperation, while others obtained…
How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model…
We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…
The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity,…
Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create challenges for conventional scientific approaches and why they…