Theory and Modern Applications
Table 5 Equilibria \(E_{i}, i=0,1,2\), and \(E^{*}\) of system (4) with \(\tau =0\)
From: Stability and bifurcation in a Holling type II predator–prey model with Allee effect and time delay
\(0< a< a_{1}\) | \(E_{0}\) GAS, \(E_{1}\), \(E_{2}\), and \(E^{*}\) do not exist | ||
\(Q_{0}\leq 0\) | \(a>a_{1}\) | \(E_{0}\) LAS, \(E_{1}\) LAS, \(E_{2}\) unstable, \(E^{*}\) does not exist | |
\(Q_{0}>0\) | \(A\geq \frac{b(x^{*})^{2}}{d}\) | \(a_{1}< a\leq a_{2}\) | \(E_{0}\) GAS, \(E_{1}\) and \(E_{2}\) unstable, \(E^{*}\) does not exist |
\(a>a_{2}\) | \(E_{0}\) LAS, \(E_{1}\), \(E_{2}\) and \(E^{*}\) unstable | ||
\(A=\frac{b(x^{*})^{2}}{d}\) | \(a>a_{1}\) | \(E_{0}\) LAS, \(E_{1}\), \(E_{2}\) and \(E^{*}\) unstable | |
\(A<\frac{b(x^{*})^{2}}{d}\) | \(a_{1}< a< a_{2}\) | \(E_{0}\) LAS, \(E_{1}\) LAS, \(E_{2}\) unstable, \(E^{*}\) does not exist | |
\(a_{2}< a< a_{3}\) | \(E_{0}\) LAS, \(E_{1}\) and \(E_{2}\) unstable, \(E^{*}\) LAS | ||
\(a>a_{3}\) | \(E_{0}\) LAS, \(E_{1}\), \(E_{2}\), and \(E^{*}\) unstable | ||