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Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays

M. Adimy, F. Crauste, A. El Abdllaoui (2010)

Mathematical Modelling of Natural Phenomena

We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takes into account a finite number of stages in blood production, characterized by cell maturity levels, which enhance the difference, in the hematopoiesis process, between dividing cells that differentiate (by going to the next stage) and dividing cells that keep the same maturity level (by staying in the same stage). It is described by a system of n nonlinear differential equations with n delays. We study...

Asymptotic stability condition for stochastic Markovian systems of differential equations

Efraim Shmerling (2010)

Mathematica Bohemica

Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by d X ( t ) = A ( ξ ( t ) ) X ( t ) d t + H ( ξ ( t ) ) X ( t ) d w ( t ) , where ξ ( t ) is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.

Banach function spaces and exponential instability of evolution families

Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu (2003)

Archivum Mathematicum

In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families.

Boundedness and stability in third order nonlinear differential equations with multiple deviating arguments

Moussadek Remili, Lynda D. Oudjedi (2016)

Archivum Mathematicum

In this paper, we establish some new sufficient conditions which guarantee the stability and boundedness of solutions of certain nonlinear and non autonomous differential equations of third order with delay. By defining appropriate Lyapunov function, we obtain some new results on the subject. By this work, we extend and improve some stability and boundedness results in the literature.

Bounds of the matrix eigenvalues and its exponential by Lyapunov equation

Guang-Da Hu, Taketomo Mitsui (2012)

Kybernetika

We are concerned with bounds of the matrix eigenvalues and its exponential. Combining the Lyapunov equation with the weighted logarithmic matrix norm technique, four sequences are presented to locate eigenvalues of a matrix. Based on the relations between the real parts of the eigenvalues and the weighted logarithmic matrix norms, we derive both lower and upper bounds of the matrix exponential, which complement and improve the existing results in the literature. Some numerical examples are also...

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