Local and global Hopf bifurcation in a neutral population model with age structure

Abstract

In this paper, an age‐structured population model with the form of neutral functional differential equation is studied. We discuss the stability of the positive equilibrium by analyzing the characteristic equation. Local Hopf bifurcation results are also obtained by choosing the mature delay as bifurcation parameter. On the center manifold, the normal form of the Hopf bifurcation is derived, and explicit formulae for determining the criticality of bifurcation are theoretically given. Moreover, the global continuation of Hopf bifurcating periodic solutions is investigated by using the global Hopf bifurcation theory of neutral equations. Finally, some numerical examples are carried out to support the main results.

Analysis of ecological shifts in the two‐age structured population model with Allee effect and environmental noise

“…The variety and complexity in behavior of population systems is associated with the nonlinear nature of interacting biological factors: the limited ecological niche, age and gender differences, the dependence of fertility on population size, interactions with other populations, and environmental influences. 5,[39][40][41][42][43][44][45] In mathematical modeling, one of the well-known is the Ricker map taking into account the carrying capacity of the environment. [46][47][48] In the present paper, these factors are studied on the base of Ricker-type model taking into account two-age structure (juveniles and adults), Allee effect, and environmental noise in the form of random immigration/emigration.…”