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Su, Ying; Wan, Aying; Wei, Junjie

Bifurcation analysis in a diffusive ‘food-limited’ model with time delay. (English) Zbl 1201.35037

Appl. Anal. 89, No. 7, 1161-1181 (2010).
The authors investigate the dynamics of a diffusive population model with delay, Dirichlet boundary condition and food-limitation. Existence of positive steady state bifurcation is established by applying phase plane ideas. The occurrence of Hopf bifurcation and of the phenomenon that the unstable positive equilibrium state without dispersion may become stable with dispersion under certain conditions, which are found by analysing the distribution of the eigenvalues. An algorithm to determine the direction and stability of the Hopf bifurcations is derived. Numerical results are given to illustrate the theoretical results.
Reviewer: Laura Iulia Aniţa (Iaşi)

Cited in 11 Documents

MSC:

35B32 Bifurcations in context of PDEs
35K57 Reaction-diffusion equations
92B05 General biology and biomathematics
35R10 Partial functional-differential equations
35B35 Stability in context of PDEs

Keywords:

Hopf bifurcation; Dirichlet boundary condition; positive steady state bifurcation
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