On positive solutions and the Omega limit set for a class of delay differential equations
- Resource Type
- Working Paper
- Authors
- Zhuge, Changjing; Sun, Xiaojuan; Lei, Jinzhi
- Source
- Discrete and Continuous Dynamical System-B, 18(2013), 2487-2503
- Subject
- Mathematics - Classical Analysis and ODEs
34K90, 92D25
- Language
This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation.
Comment: 15 pages, 2 figures