# American Institute of Mathematical Sciences

November  2013, 18(9): 2487-2503. doi: 10.3934/dcdsb.2013.18.2487

## On positive solutions and the Omega limit set for a class of delay differential equations

 1 Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China 2 School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China 3 Zhou Pei-Yuan Center for Applied Mathematics, MOE Key Laboratory of Bioinformatics, Tsinghua University, Beijing, 100084, China

Received  March 2013 Revised  May 2013 Published  September 2013

This paper studies positive solutions of a class of delay differential equations of two delays that are originated from a mathematical model of hematopoietic dynamics. We give an optimal condition on initial conditions for $t\leq 0$ such that the solutions are positive for $t>0$. Long time behaviors of these positive solutions are also discussed through a dynamical system defined at a space of continuous functions. Characteristic description of the $\omega$ limit set of this dynamical system is obtained. This $\omega$ limit set provides informations for the long time behaviors of positive solutions of the delay differential equation.
Citation: Changjing Zhuge, Xiaojuan Sun, Jinzhi Lei. On positive solutions and the Omega limit set for a class of delay differential equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2487-2503. doi: 10.3934/dcdsb.2013.18.2487
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