Number of positive periodic solutions for feedback-driven nonlinear differential equation: application to hematopoietic process.

This paper considers a first-order nonlinear differential equation that driven by feedback dominated by time delays. Sufficient conditions which determine the number of positive periodic solutions are studied. Our findings give insight into the existence of positive periodic solutions by exploring the Δ -points and ∇ -points that are specifically defined. Moreover, a numerical example and its simulations are provided to illustrate our main results. In this example, at least four positive periodic solutions are ensured by our results. The existence regions of these four positive periodic solutions are also clarified. Finally, we discuss the hematopoietic process (the production process of blood cells) to demonstrate the application of the theoretical results. [ABSTRACT FROM AUTHOR]