Periodic oscillations in age-structured ratio-dependent predator–prey model with Michaelis–Menten type functional response

A novel Michaelis–Menten type ratio-dependent predator–prey model with predator-age structure is investigated. The predator fertility function is considered to be the piecewise function related to predator maturation period τ. Our methods rely upon integrated semigroup theory and Hopf bifurcation theory for semilinear equations with non-dense domain. By local analysis and bifurcation analysis of the model, a non-trivial periodic oscillation phenomenon through Hopf bifurcation appears when parameter τ passes through some critical values. Numerical simulations and sensitivity analysis on several important parameters are also performed to illustrate the conclusions.