Hopf bifurcations of some second-order FDEs with infinite delay and their applications
The general existence criteria for Hopf bifurcation are applied to the predator-prey system with infinite delay \(\dot N(t) = rN(t) [1 - bN(t) - cp(t)]\), \(\dot p(t) = p(t) [-d + \int^0_{- \infty} K (\tau)\). \(N (t + \tau) [e + \gamma N (t + \tau)]^{-1} d \tau]\), where \(K (\tau) \geq 0\) is real, \(\int^0_{- \infty} K(s)ds = \ell < + \infty\), \(r,b,c,d,e > 0\), \(\gamma > 0\) and \(\ell > (\gamma + ab) d\). The existence of a Hopf bifurcation is established, the bifurcation direction is determined and the stability of bifurcating periodic solutions is proved.
predator-prey system with infinite delay
stability of bifurcating periodic solutions
scientific article; zbMATH DE number 783489