Loading [MathJax]/extensions/MathZoom.js
Skeletal patterning in the vertebrate limb,
i.e., the spatiotemporal regulation of cartilage differentiation
(chondrogenesis) during embryogenesis and regeneration, is one
of the best studied examples of a multicellular developmental process.
Recently [Alber et al., The morphostatic limit for a model of
skeletal pattern formation in the vertebrate limb, Bulletin of
Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation
reaction-diffusion system was developed to describe the interaction...
Vasculogenesis and angiogenesis are two different mechanisms for blood vessel formation. Angiogenesis occurs when new vessels sprout from pre-existing vasculature in response to external chemical stimuli. Vasculogenesis occurs via the reorganization of randomly distributed cells into a blood vessel network. Experimental models of vasculogenesis have suggested that the cells exert traction forces onto the extracellular matrix and that these forces may play an important role in the network forming...
Vasculogenesis and angiogenesis are two different mechanisms for blood
vessel formation. Angiogenesis occurs when new vessels sprout from
pre-existing vasculature in response to external chemical stimuli.
Vasculogenesis occurs via the reorganization of randomly distributed
cells into a blood vessel network. Experimental models
of vasculogenesis have suggested that the cells exert traction forces
onto the extracellular matrix and that these forces may play
an important role in the network forming...
A conceptual minimal model demonstrating spatially heterogeneous wave regimes
interpreted as pursuit-evasion in predator-prey system is constructed and investigated. The
model is based on the earlier proposed hypothesis that taxis accelerations of prey and
predators are proportional to the density gradient of another population playing a role
of taxis stimulus. Considering acceleration rather than immediate velocity allows
obtaining realistic solutions even while ignoring variations of total...
Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces.
In this paper we investigate a mathematical model that has been
shown to display these structures when solved numerically. The model consists of an ordinary
differential equation coupled with a partial differential equation involving a first-order
hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to
admit global weak solutions.
Recently, adult stem cells have become a focus of intensive biomedical research, but the
complex regulation that allows a small population of stem cells to replenish depleted tissues is still
unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells
undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that
a feedback control of stem cells on their own proliferation and differentiation (denoted Quorum
Sensing) suffices...
The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter , which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries....
Plants and animals have highly ordered structure both in time and in space, and one of the main questions of modern developmental biology is the transformation of genetic information into the regular structure of organism. Any multicellular plant begins its development from the universal unicellular state and acquire own species-specific structure in the course of cell divisions, cell growth and death, according to own developmental program. However the cellular mechanisms of plant development are...
A mathematical model of the microalgal growth under various light regimes is required for the optimization of design parameters and operating conditions in a photobioreactor. As its modelling framework, bilinear system with single input is chosen in this paper. The earlier theoretical results on bilinear systems are adapted and applied to the special class of the so-called intermittent controls which are characterized by rapid switching of light and dark cycles. Based on such approach, the following...
The nonlocal Fisher equation has been proposed as a simple model exhibiting Turing
instability and the interpretation refers to adaptive evolution. By analogy with other formalisms
used in adaptive dynamics, it is expected that concentration phenomena (like convergence to a sum
of Dirac masses) will happen in the limit of small mutations. In the present work we study this
asymptotics by using a change of variables that leads to a constrained Hamilton-Jacobi equation.
We prove the convergence analytically...
We show the location of so called critical points, i.e., couples of diffusion coefficients for which a non-trivial solution of a linear reaction-diffusion system of activator-inhibitor type on an interval with Neumann boundary conditions and with additional non-linear unilateral condition at one or two points on the boundary and/or in the interior exists. Simultaneously, we show the profile of such solutions.
The dynamics of an activator-inhibitor model with general cubic polynomial source is investigated. Without diffusion, we consider the existence, stability and bifurcations of equilibria by both eigenvalue analysis and numerical methods. For the reaction-diffusion system, a Lyapunov functional is proposed to declare the global stability of constant steady states, moreover, the condition related to the activator source leading to Turing instability is obtained in the paper. In addition, taking the...
Currently displaying 1 –
20 of
47