Global dynamics and Hopf bifurcation of a structured population model

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Abstract

In this paper, we consider a system of delay differential equations which describes a structured single species population distributed over a two-patch environment. For a large class of birth functions, we obtain sufficient conditions for uniform persistence and global stabilities of equilibria. A Hopf bifurcation in this system is also discussed when the birth function takes a specific form, and the stability of the bifurcated periodic solutions and the bifurcation direction are investigated in detail. Finally, some numerical simulations of the system are given. © 2004 Elsevier Ltd. All rights reserved.

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Xu, D. (2005). Global dynamics and Hopf bifurcation of a structured population model. Nonlinear Analysis: Real World Applications, 6(3), 461–476. https://doi.org/10.1016/j.nonrwa.2003.12.003

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