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Theory and Modern Applications

Table 3 Equilibria \(E_{i}, i=0,1,2\), of system (4)

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, \(E_{1}\) and \(E_{2}\) do not exist

\(Q_{0}\leq 0\)

\(a>a_{1}\)

\(E_{0}\) LAS, \(E_{1}\) LAS, \(E_{2}\) unstable

\(Q_{0}>0\)

\(A\geq \frac{b(x^{*})^{2}}{d}\)

\(a>a_{1}\)

\(E_{0}\) LAS, \(E_{1}\) unstable, \(E_{2}\) unstable

\(A<\frac{b(x^{*})^{2}}{d}\)

\(a_{1}< a< a_{2}\)

\(E_{0}\) LAS, \(E_{1}\) LAS, \(E_{2}\) unstable

\(a>a_{2}\)

\(E_{0}\) LAS, \(E_{1}\) unstable, \(E_{2}\) unstable