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2005, Volume 5, Issue 3: 735-752. Doi: 10.3934/dcdsb.2005.5.735
This issue Previous Article Effective Hamiltonian for traveling discrete breathers in the FPU chain Next Article Nonisothermal phase separation based on a microforce balance

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

  • 1.

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

Received:  January 2004
Revised:  July 2004
Published:  August 2005
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: 82D10, 76X05, 35B60, 35B40.

    Citation:
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