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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 behaviour of the equation $\dot{z} = G (t, z) [h (z) + g (t, z)]$

Josef Kalas (1989)

Archivum Mathematicum

Asymptotic instability of nonlinear differential equations.

Avis, Rafael, Naulin, Raúl (1997)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Asymptotic properties of the solutions of the equation $\dot{z} = f (t, z)$ with a complex-valued function $f$

Josef Kalas (1981)

Archivum Mathematicum

Asymptotic stability and instability with respect to part of variables for solutions to impulsive systems.

Ignat'ev, A.O. (2008)

Sibirskij Matematicheskij Zhurnal

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.

Asymptotic stability of switching systems.

Boularas, Driss, Cheban, David (2010)