Table 4 Eigenvalues and stability analysis of the jacobian matrix at equilibrium points.
Point of equilibrium | Eigenvalues \(\varvec{\lambda }_{\textbf{1}}\) | Eigenvalues \(\varvec{\lambda }_{\textbf{2}}\) | Eigenvalues \(\varvec{\lambda }_{\textbf{3}}\) |
|---|---|---|---|
\(E_1(0,0,0)\) | \(M+R\) | \(T-D_2\) | \(Q-L_2\) |
\(E_2(0,0,1)\) | \(M+R+L_1-L_2\) | \(N+T-D_2\) | \(L_2-Q\) |
\(E_3(0,1,0)\) | \(M+R+K_1-K_2\) | \(-\left( T-D_2\right)\) | \(-L_2+\beta G_2-N+Q\) |
\(E_4(0,1,1)\) | \(M+R+K_1-K_2+L_1-L_2\) | \(-\left( N+T-D_2\right)\) | \(L_2-\beta G_2+N-Q\) |
\(E_5(1,0,0)\) | \(-(M+R)\) | \(-D_1\) | \(Q-L_1\) |
\(E_6(1,0,1)\) | \(-\left( M+R+L_1-L_2\right)\) | \(N -D_1\) | \(L_1-Q\) |
\(E_7(1,1,0)\) | \(-\left( M+R+K_1-K_2\right)\) | \(D_1\) | \(-L_1-N+Q\) |
\(E_8(1,1,1)\) | \(-\left( M+R+K_1-K_2+L_1-L_2\right)\) | \(-\left( N-D_1\right)\) | \(L_1+N-Q\) |
