Bifurcations of an age structured predator-prey model with time delays (Q2892405)

The authors study an age structured predator-prey model with time delays. For a simplified case, the population dynamics is essentially determined by the system NEWLINE\[NEWLINEx'(t) = rx(t)[1 - x(t)/K - \beta y(t)],\;y'(t) = \mu\beta x(t -\tau)y(t -\tau) -d y(t),NEWLINE\]NEWLINE where \(r\), \(K\), \(\mu\), \(\beta\), \(\tau\) and \(d\) are all positive constants. Sufficient conditions are found for the existence and asymptotic stability of a positive equilibrium, and it is shown that the system undergoes a Hopf bifurcation at the positive equilibrium when the delay \(\tau\) takes some particular values.