Slowly oscillating periodic solutions for the Nicholson's blowflies equation with state‐dependent delay |
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| Authors: | Ling Zhang Shangjiang Guo |
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| Affiliation: | 1. School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei, China;2. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, China |
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| Abstract: | In this paper, we study the dynamics of a Nicholson's blowflies equation with state‐dependent delay. For the constant delay, it is known that a sequence of Hopf bifurcation occurs at the positive equilibrium as the delay increases and global existence of periodic solutions has been established. Here, we consider the state‐dependent delay instead of the constant delay and generalize the results on the existence of slowly oscillating periodic solutions under a set of mild conditions on the parameters and the delay function. In particular, when the positive equilibrium gets unstable, a global unstable manifold connects the positive equilibrium to a slowly oscillating periodic orbit. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | Nicholson's blowflies state‐dependent delay slowly oscillating solutions discrete Lyapunov functional unstable manifold |
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