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Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models

J. Clairambault, S. Gaubert, Th. Lepoutre (2009)

Mathematical Modelling of Natural Phenomena

We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in mice endowed with intact or disrupted circadian clocks, known to exert their influence on the cell division cycle. We compare the growth rate of the model controlled by a time-periodic control on its coefficients with the growth rate of stationary models of the same nature, but with averaged coefficients....

Comparison of six models of antiangiogenic therapy

Andrzej Świerniak (2009)

Applicationes Mathematicae

Six models of antiangiogenic therapy are compared and analyzed from control-theoretic point of view. All of them consist of a model of tumor growth bounded by the capacity of a vascular network developed by the tumor in the process of angiogenesis and different models of dynamics of this network, and are based on the idea proposed by Hahnfeldt et al. Moreover, we analyse optimal control problems resulting from their use in treatment protocol design.

Comparison of supervised learning methods for spike time coding in spiking neural networks

Andrzej Kasiński, Filip Ponulak (2006)

International Journal of Applied Mathematics and Computer Science

In this review we focus our attention on supervised learning methods for spike time coding in Spiking Neural Networks (SNNs). This study is motivated by recent experimental results regarding information coding in biological neural systems, which suggest that precise timing of individual spikes may be essential for efficient computation in the brain. We are concerned with the fundamental question: What paradigms of neural temporal coding can be implemented with the recent learning methods? In order...

Compartmental Models of Migratory Dynamics

J. Knisley, T. Schmickl, I. Karsai (2011)

Mathematical Modelling of Natural Phenomena

Compartmentalization is a general principle in biological systems which is observable on all size scales, ranging from organelles inside of cells, cells in histology, and up to the level of groups, herds, swarms, meta-populations, and populations. Compartmental models are often used to model such phenomena, but such models can be both highly nonlinear and difficult to work with.Fortunately, there are many significant biological systems that are amenable to linear compartmental models which are often...

Competition of Species with Intra-Specific Competition

N. Apreutesei, A. Ducrot, V. Volpert (2008)

Mathematical Modelling of Natural Phenomena

Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom....

Competitive Exclusion in a Discrete Stage-Structured Two Species Model

A. S. Ackleh, P. Zhang (2009)

Mathematical Modelling of Natural Phenomena

We develop a stage-structured model that describes the dynamics of two competing species each of which have sexual and clonal reproduction. This is typical of many plants including irises. We first analyze the dynamical behavior of a single species model. We show that when the inherent net reproductive number is smaller than one then the population will go to extinction and if it is larger than one then an interior equilibrium exists and it is globally asymptotically stable. Then we analyze...

Computer Simulation of Protein-Protein Association in Photosynthesis

I.B. Kovalenko, A.M. Abaturova, A.N. Diakonova, O.S. Knyazeva, D.M. Ustinin, S.S. Khruschev, G.Yu. Riznichenko, A.B. Rubin (2011)

Mathematical Modelling of Natural Phenomena

The paper is devoted to the method of computer simulation of protein interactions taking part in photosynthetic electron transport reactions. Using this method we have studied kinetic characteristics of protein-protein complex formation for four pairs of proteins involved in photosynthesis at a variety of ionic strength values. Computer simulations describe non-monotonic dependences of complex formation rates on the ionic strength as the result of...

Currently displaying 421 – 440 of 1850