Hopf bifurcations in a reaction-diffusion population model with delay effect

By Ying-Chin Su, Junjie Wei, Junping Shi. 2009

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Hopf bifurcation in a delayed reaction-diffusion-advection population model (2017, background): “Then, we can obtain the similar results as the case of spatial homogeneity [2, 33]: for λ ∈ (λ∗, λ ], where 0 < λ − λ∗ ≪ 1, there exists a sequence of values {τn(λ)} ∞ n=0, such that, when τ = τn(λ), Eq.”
Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect (2012, methodology): “Our main results in this paper is in the spirit of [4,36] for the local growth rate case: for a general bounded domain Ω , there exists a λ∗ satisfying 0 < λ∗ − λ∗ 1, such that for any λ ∈ (λ∗, λ∗], Eq.”
Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect (2015, background): “Hopf bifurcating periodic solutions can be found by means of a center manifold (see, for example, [3,5,12,14]).”