Bifurcation analysis for a regulated logistic growth model |
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Authors: | Yongli Song Sanling Yuan |
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Institution: | 1. Department of Mathematics, Tongji University, 1239 Siping Road, Shanghai 200092, China;2. Department of Basic Sciences, University of Shanghai for Science and Technology, Shanghai 200093, China |
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Abstract: | In this paper, we consider a regulated logistic growth model. We first consider the linear stability and the existence of a Hopf bifurcation. We show that Hopf bifurcations occur as the delay τ passes through critical values. Then, using the normal form theory and center manifold reduction, we derive the explicit algorithm determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions. Finally, numerical simulation results are given to support the theoretical predictions. |
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Keywords: | 34K18 92D25 |
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