相关论文: Stability Analysis of Population Dynamics Model in…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
We explore the emergence of cooperation in the framework of evolutionary game theory. First we introduce the cooperation problem in a novel way that we believe it have important consequences in how problem is addressed. Then we present a…
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium…
Biofilms are communities of microorganisms that grow on virtually all surfaces with sufficient nutrients including aquatic and industrial water systems and medical devices. Biofilms are complex, structured communities where the interplay of…
We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…
The spread of new products in a networked population is often modeled as an epidemic. However, in the case of `complex' contagion, these models {do not capture nuanced, dynamic social reinforcement effects in adoption behavior}. In this…
To explore the coupling between a growing population of microorganisms such as E. coli and a nonuniform nutrient distribution, we formulate a minimalistic model. It consists of active Brownian particles that divide and grow at a…
A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole.…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe the co-evolution of strategic actions of a population of individuals and the state of the surrounding environment;…
We study the steady states and dynamics of a thin film-type equation with non-conserved mass in one dimension. The evolution equation is a nonlinear fourth-order degenerate parabolic PDE motivated by a model of volatile viscous fluid films…
Anisotropic collective patterns occur frequently in the morphogenesis of 2D biofilms. These patterns are often attributed to growth regulation mechanisms and differentiation based on gradients of diffusing nutrients and signalling…
From multicellular tissues to bacterial colonies, three dimensional cellular structures arise through the interaction of cellular activities and mechanical forces. Simple bacterial communities provide model systems for analyzing such…
We investigate the structure and stability of the steady states for a bacterial colony model with density-suppressed motility. We treat the growth rate of bacteria as a bifurcation parameter to explore the local and global structure of the…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
In this work we consider a size-structured cannibalism model with the model ingredients (fertility, growth, and mortality rate) depending on size (ranging over an infinite domain) and on a general function of the standing population…
Growing tissue and bacterial colonies are active matter systems where cell divisions and cellular motion generate active stress. Although they operate in the non-equilibrium regime, these biological systems can form large-scale ordered…