Theory and Modern Applications
Table 6 System (4) with \(Q_{0}>0\) and \(A<\frac{b(x^{*})^{2}}{d}\)
From: Stability and bifurcation in a Holling type II predator–prey model with Allee effect and time delay
Birth rate a | Equilibria |
|---|---|
\(0< a< a_{1}\) | \(E_{0}\) GAS, \(E_{1}\), \(E_{2}\), and \(E^{*}\) do not exist |
\(a_{1}< a< a_{2}\) | \(E_{0}\) and \(E_{1}\) LAS, \(E_{2}\) unstable, \(E^{*}\) does not exist |
\(a_{2}< a\leq a_{4}\) | \(E_{0}\) LAS, \(E_{1}\) and \(E_{2}\) unstable, \(E^{*}\) LAS |
\(a_{4}< a< a_{3}\) | \(E_{0}\) LAS, \(E_{1}\) and \(E_{2}\) unstable, \(E^{*}\) exists a Hopf bifurcation |