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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 290287, 2 pages
Periodic Solution of the Hematopoiesis Equation
National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou 215123, China
Received 4 December 2012; Accepted 30 December 2012
Copyright © 2013 Ji-Huan He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Wu and Liu (2012) presented some results for the existence and uniqueness of the periodic solutions for the hematopoiesis model. This paper gives a simple approach to find an approximate period of the model.
Equation (1) admits periodic solutions as revealed in . Hereby we suggest a simple approach to the search for an approximate period of (1) using a simple amplitude-frequency formulation [2–5]. To this end, we rewrite (1) in the form
Assume that the periodic solution can be expressed in the form
Setting , , and , , respectively, we have
This formulation has been widely used to solve periodic solutions of various nonlinear oscillators [6–13], and it is often called as He’s frequency formulation, He’s amplitude-frequency formulation, or He’s frequency-amplitude formulation. In case , no period solution is admitted. A similar criterion is given for a nonlinear equation arising in electrospinning process .
The work is supported by PAPD (a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions), National Natural Science Foundation of China under Grant no. 10972053, and Project for Six Kinds of Top Talents in Jiangsu Province, China (Grant no. ZBZZ-035).
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