Related papers: On discretely structured growth models and their m…
A model for morphoelastic growth, that is, growth influenced by elastic stress, driven by the absorption of nutrients is considered. The model features a multiplicative decomposition of the deformation gradient into an elastic contribution…
In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…
Selection of a phenotypical trait can be described in mathematical terms by 'stage structured' equations which are usually written under the form of integral equations so as to express competition for resource between individuals whatever…
In this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in…
Moment closure on general discrete structures often requires one of the following: (i) an absence of short closed loops (zero clustering); (ii) existence of a spatial scale; (iii) ad hoc assumptions. Algebraic methods are presented to avoid…
The logistic differential equation is used to analyze cancer cell population, in the presence of a correlated Gaussian white noise. We study the steady state properties of tumor cell growth and discuss the effects of the correlated noise.…
Existence and uniqueness of solutions for a class of models for stress-modulated growth is proven in one spatial dimension. The model features the multiplicative decomposition of the deformation gradient $F$ into an elastic part $F_e$ and a…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…
Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible…
We consider a periodic extension of the classical Kingman non-linear model (Kingman, 1978) for the balance between selection and mutation in a large population. In the original model, the fitness distribution of the population is modeled by…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
We investigate a model for the accretive growth of an elastic solid. The reference configuration of the body is accreted in its normal direction, with space- and deformation-dependent accretion rate. The time-dependent reference…
A birth-death lattice gas model about the influence of an environment on the fitness and concentration evolution of economic entities is analytically examined. The model can be mapped onto a high order logistic map. The control parameter is…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…
This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…
Species sharing a habitat will co-evolve to make use of the available resources, as consumption is modulated by competition and negative feedback loops between consumers and resources. The dietary range of a given species determines the…