Theory and Modern Applications
From: Impact of the fear and Allee effect on a Holling type II prey–predator model
Equilibrium | Existence | Type |
---|---|---|
\(B_{0}(0,0)\) | Always exists | Locally asymptotically stable; |
\(a>\max \{a_{1},a_{3}\}\), Globally asymptotically stable. | ||
\(B_{1}(x_{1},0)\) | \(0< a< a_{1}\) | \(0< a< a_{1}\) and \(0< b< b_{1}\), Unstable; |
\(0< a< a_{1}\) and \(b>b_{1}\), Saddle. | ||
\(B_{2}(x_{2},0)\) | \(0< a< a_{1}\) | \(0< a< a_{1}\) and \(0< b< b_{2}\), Saddle; |
\(0< a< a_{1}\) and \(b>b_{2}\), Locally asymptotically stable. | ||
\(B^{*}(x^{*},y^{*})\) | \(r>r_{1}\) and \(ce>bd_{2}\) | \(0< a< a_{2}\) and \(r_{1}< r\leq r_{2}\), Locally asymptotically stable; |
\(0< a< a_{2}\) and \(r>r_{2}\) and \(f>f_{1}\), Locally asymptotically stable; | ||
\(a\geq a_{2}\) and \(r>r_{1}\), Unstable; | ||
\(0< a< a_{2}\) and \(r>r_{2}\) and \(0< f< f_{1}\), Unstable. |