Bounded global Hopf branches for stage-structured differential equations
舒洪英 特聘研究员 (同济大学)
Abstract. We consider a class of stage-structured differential equations. By using the time delay as a bifurcation parameter, we show that the number of local Hopf bifurcation values is finite. Furthermore, we analytically prove that these local Hopf bifurcation values are neatly paired, and each pair is jointed by a bounded global Hopf branch. We use the well-known Mackey–Glass equation with a stage structure as an illustrative example to demonstrate that bounded global Hopf branches can induce interesting and rich dynamics. At last, we extend the bounded global Hopf branches theorem to a delayed reaction-diffusion population model with unimodal feedback and stage-structure.