Highlights• Consider a predator-prey model with age structure • Rewrite the age structured model as a non-densely defined Cauchy problem.• The stability and Hopf bifurcation are studied.• The numerical simulations support our results.
AbstractA predator-prey model is investigated in which the predator population is assumed to have an age structure. We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness of positive age-dependent equilibrium for the model. Bifurcation analysis indicates that the predator-prey system with age structure exhibits Hopf bifurcation which is the main result of this paper. Numerical simulations are given to illustrate the given results.
This paper is devoted to the study of a spatially and age structured population dynamics model. We study the stability and Hopf bifurcation of the positive equilibrium of the model by using a bifurcation theory in the context of integrated semigroups. This problem is a first example for Hopf bifurcation for a spatially and age/size structured population dynamics model. Bifurcation analysis indicates that Hopf bifurcation occurs at a positive age/size dependent steady state of the model. The results are confirmed by some numerical simulations.2010 Mathematics Subject Classification. 37L10, 37G15, 35B32, 35K55, 92D25.
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