Table 11 Stability conditions for Equilibrium points
Equilibrium point | \(\textrm{DET}(\textrm{J})\) | \(\textrm{Tr}\left(\textrm{J}\right)\) | Equilibrium condition |
|---|---|---|---|
P0 | \({r}_{1}{r}_{2}\) | \({r}_{1}{+r}_{2}\) | Disequilibrium |
P1 | \(DET\left(J\left(P1\right)\right)\) | \(-\left({r}_{1}{+r}_{2}\right)\) | \(\alpha +\beta>1\) |
P2 | \(DET\left(J\left(P2\right)\right)\) | \(-\left({r}_{1}{+r}_{2}\right)\) | \(\alpha +\beta <1\) |
P3 | \({-r}_{1}{r}_{2}\) | \(-\left({r}_{1}{+r}_{2}\right)\) | Disequilibrium |
P4 | \({-r}_{1}{r}_{2}\) | \({r}_{1}{-r}_{2}\) | Disequilibrium |