×

zbMATH — the first resource for mathematics

Existence and exponential stability of positive almost periodic solutions for a model of hematopoiesis. (English) Zbl 1186.34116
The authors consider the following hematopoiesis equation with impulses \[ \begin{cases} h^{\prime}(t)=-\alpha(t)h(t)+\frac{\beta(t)}{1+h^n(t-\tau)},&t\not=\theta_k,\\ \Delta(\theta_k):=h(\theta_k^+)-h(\theta_k^-)=\gamma_kh(\theta_k^-)+\delta_k,&k\in \mathbb{N}. \end{cases}\tag{1} \]
Sufficient conditions for the existence of a positive almost periodic solution \(p(t)\) and its exponential stability are obtained.

MSC:
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K45 Functional-differential equations with impulses
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[5] doi:10.1016/j.cam.2005.06.004 · Zbl 1101.34065
[6] doi:10.1016/j.jmaa.2005.04.005 · Zbl 1110.34019
[8] doi:10.1142/S0219525908001519 · Zbl 1168.34052
[9] doi:10.1016/j.jmaa.2003.11.061 · Zbl 1062.34055
[10] doi:10.1016/j.nonrwa.2007.05.004 · Zbl 1154.34394
[12] doi:10.1016/S0895-7177(04)90519-5 · Zbl 1065.92066
[13] doi:10.1016/j.nonrwa.2007.10.022 · Zbl 1167.34318
[14] doi:10.1016/S0096-3003(02)00315-6 · Zbl 1048.34114
[15] doi:10.1016/j.jmaa.2006.12.015 · Zbl 1155.34041
[17] doi:10.1016/j.jmaa.2006.12.015 · Zbl 1155.34041
[20] doi:10.1016/j.amc.2007.01.103 · Zbl 1131.34327
[21] doi:10.1016/j.mcm.2008.07.014 · Zbl 1171.34344
[22] doi:10.1371/journal.pcbi.1000268
[25] doi:10.1016/j.amc.2006.09.133 · Zbl 1113.92070
[26] doi:10.1016/j.amc.2007.03.048 · Zbl 1193.34146
[27] doi:10.1016/j.amc.2007.04.044 · Zbl 1193.34158
[28] doi:10.1016/j.chaos.2006.05.003 · Zbl 1152.34343
[29] doi:10.1016/S0096-3003(01)00274-0 · Zbl 1035.34080
[30] doi:10.1016/j.nonrwa.2008.10.015 · Zbl 1225.47072
[31] doi:10.1016/j.nonrwa.2008.09.003 · Zbl 1170.45004
[32] doi:10.1016/j.nonrwa.2008.02.020 · Zbl 1162.34349
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.