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Theory and Modern Applications

Table 1 Equilibria of system (4)

From: Stability and bifurcation in a Holling type II predator–prey model with Allee effect and time delay

\(0< a< a_{1}\)

\(E_{0}\) exists

\(Q_{0}\leq 0\)

\(a>a_{1}\)

\(E_{0}\), \(E_{1}\), \(E_{2}\) exist

\(Q_{0}>0\)

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

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

\(E_{0}\), \(E_{1}\), \(E_{2}\) exist

\(a>a_{2}\)

\(E_{0}\), \(E_{1}\), \(E_{2}\), \(E^{*}\) exist

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

\(a>a_{1}\)

\(E_{0}\), \(E_{1}\), \(E_{2}\), \(E^{*}\) exist