Table 3 Eigenvalues of the linearized matrix for the autonomous system’s critical points when \(\alpha \) is positive.
From: Dynamical system analysis of interacting dark energy in LRS Bianchi type I cosmology
Points | \(\lambda _{1}\) | \(\lambda _{2}\) | \(\lambda _{3}\) |
|---|---|---|---|
A | \(3+\alpha \) | \(3-\frac{3\lambda \sqrt{2n+1}}{\sqrt{2}(n+2)}\) | \(3+\alpha \) |
B | \(3+\alpha \) | \(3+\frac{3\lambda \sqrt{2n+1}}{\sqrt{2}(n+2)}\) | \(3+\alpha \) |
C | \((\alpha -3)+\frac{3\lambda ^{2}(2n+1)}{(n+2)^{2}}\) | \(\frac{9\lambda ^{2}(2n+1)}{(n+2)^{2}}\bigg [\frac{\lambda ^{2}(2n+1)}{2(n+2)^{2}}-1\bigg ]\) | \(\frac{9\lambda ^{2}(2n+1)}{2(n+2)^{2}}-4\) |
D | \((\alpha -3)+\frac{3\lambda ^{2}(2n+1)}{(n+2)^{2}}\) | \(\frac{9\lambda ^{2}(2n+1)}{(n+2)^{2}}\bigg [\frac{\lambda ^{2}(2n+1)}{2(n+2)^{2}}-1\bigg ]\) | \(\frac{9\lambda ^{2}(2n+1)}{2(n+2)^{2}}-4\) |
E | \((\alpha -3)+\frac{(\alpha -3)^{2}(n+2)^{2}}{3\lambda ^{2}(2n+1)}\) | 3 | \(-2\) |
F | \((\alpha -3)+\frac{(\alpha -3)^{2}(n+2)^{2}}{3\lambda ^{2}(2n+1)}\) | \(-\frac{4}{9}\) | \(-1\) |
