142 research outputs found
Stability analysis of cell dynamics in leukemia
In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations. © 2012 EDP Sciences
Stability of fractional neutral systems with multiple delays and poles asymptotic to the imaginary axis
This paper addresses the H∞-stability of linear fractional systems with multiple commensurate delays, including those with poles asymptotic to the imaginary axis. The asymptotic location of the neutral chains of poles are obtained, followed by the determination of conditions that guarantee a finite H∞ norm for those systems with all poles in the left half-plane of the complex plane. ©2010 IEEE
Stability Analysis of systems with distributed delays and application to hematopoietic cell maturation dynamics
We consider linear systems with distributed delays where delay kernels are assumed to be finite duration impulse responses of finite dimensional systems. We show that stability analysis for this class of systems can be reduced to stability analysis of linear systems with discrete delays, for which many algorithms are available in the literature. The results are illustrated on a mathematical model of hematopoietic cell maturation dynamics. © 2008 IEEE
Local asymptotic stability conditions for the positive equilibrium of a system modeling cell dynamics in leukemia
A distributed delay system with static nonlinearity has been considered in the literature to study the cell dynamics in leukemia. In this chapter local asymptotic stability conditions are derived for the positive equilibrium point of this nonlinear system. The stability conditions are expressed in terms of inequalities involving parameters of the system. These inequality conditions give guidelines for development of therapeutic actions. © 2012 Springer-Verlag GmbH Berlin Heidelberg
A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems
This paper aims to provide a numerical algorithm able to locate all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by giving the asymptotic position of the chains of poles and the conditions for their stability for a small delay. When these conditions are met, the root continuity argument and some simple substitutions allow us to determine the locations where some roots cross the imaginary axis, providing therefore the complete characterization of the stability windows. The same method can be extended to provide the position of all unstable poles as a function of the delay. © 2012 Elsevier Ltd. All rights reserved
Stability windows and unstable root-loci for linear fractional time-delay systems
The main point of this paper is on the formulation of a numerical algorithm to find the location of all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by the asymptotic position of the chains of poles and conditions for their stability, for a small delay. When these conditions are met, we continue by means of the root continuity argument, and using a simple substitution, we can find all the locations where roots cross the imaginary axis. We can extend the method to provide the location of all unstable poles as a function of the delay. Before concluding, some examples are presented. © 2011 IFAC
Transmission Studies of Left-handed Materials
Left-handed materials are studied numerically using an improved version of
the transfer-matrix method. The transmission, reflection, the phase of the
reflection and the absorption are calculated and compared with experiments for
both single split-ring resonators (SRR) with negative permeability and
left-handed materials (LHMs) which have both the permittivity and permeability
negative. Our results suggest ways of positively identifying materials that
have both permittivity and permeability negative, from materials that have
either permeability or permittivity negative
Radiating dipoles in photonic crystals
The radiation dynamics of a dipole antenna embedded in a Photonic Crystal are
modeled by an initially excited harmonic oscillator coupled to a non--Markovian
bath of harmonic oscillators representing the colored electromagnetic vacuum
within the crystal. Realistic coupling constants based on the natural modes of
the Photonic Crystal, i.e., Bloch waves and their associated dispersion
relation, are derived. For simple model systems, well-known results such as
decay times and emission spectra are reproduced. This approach enables direct
incorporation of realistic band structure computations into studies of
radiative emission from atoms and molecules within photonic crystals. We
therefore provide a predictive and interpretative tool for experiments in both
the microwave and optical regimes.Comment: Phys. Rev. E, accepte
Analysis of Blood Cell Production under Growth Factors Switching
Hematopoiesis is a highly complicated biological phenomenon. Improving its mathematical modeling and analysis are essential steps towards consolidating the common knowledge about mechanisms behind blood cells production. On the other hand, trying to deepen the mathematical modeling of this process has a cost and may be highly demanding in terms of mathematical analysis. In this paper, we propose to describe hematopoiesis under growth factor-dependent parameters as a switching system. Thus, we consider that different biological functions involved in hematopoiesis, including aging velocities, are controlled through multiple growth factors. Then we attempt a new approach in the framework of time-delay switching systems, in order to interpret the behavior of the system around its possible positive steady states. We start here with the study of a specific case in which switching is assumed to result from drug infusions. In a broader context, we expect that interpreting cell dynamics using switching systems leads to a good compromise between complexity of realistic models and their mathematical analysis. © 201
A coupled model for healthy and cancerous cells dynamics in Acute Myeloid Leukemia
In this paper we propose a coupled model for healthy and cancerous cell dynamics in Acute Myeloid Leukemia. The PDE-based model is transformed to a nonlinear distributed delay system. For an equilibrium point of interest, necessary and sufficient conditions of local asymptotic stability are given. Simulation examples are given to illustrate the results. © IFAC
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