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August  2005, 5(3): 735-752. doi: 10.3934/dcdsb.2005.5.735

Dynamics of a logistic population model with maturation delay and nonlinear birth rate

Suqi Ma 1, , Qishao Lu 1, and  Shuli Mei 1,

1. 

School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China, China, China

Received  January 2004 Revised  July 2004 Published  May 2005

A logistic population model with a maturation delay stage for adults is investigated. The adult population is related to its previous life stage with a maturation delay $r$, and has a non-linear exponential birth rate $be^{-pr}$ with a birth decay coefficient $p$. As $r$ increases, the unique positive equilibrium solution may experience two stability switchings, that is, from stable to unstable, and then back to stable again. The decay coefficient $p$ can also qualitatively influence the stability property of the system. Hopf bifurcation and the stability of the bifurcating periodic solution are analyzed by means of the center manifold theory and the normal form technique. By applying the integral averaging theory, phase-locked and phase-shifting solutions induced by the external excitation are also investigated and verified by numerical simulations.
Keywords: quasi-periodic solution, Hopf bifurcation., maturation delay, logistic population model, periodic solution, stability.
Mathematics Subject Classification: 82D10, 76X05, 35B60, 35B4.
Citation: Suqi Ma, Qishao Lu, Shuli Mei. Dynamics of a logistic population model with maturation delay and nonlinear birth rate. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 735-752. doi: 10.3934/dcdsb.2005.5.735
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