Table 7 The eigenvalues at each equilibrium point of Eq. (8).

E₁(0, 0, 1)

\({\it{\lambda }}_1^1 = {\it{a}} - {\it{b}}\), \({\it{\lambda }}_1^2 = {\it{d}} - {\it{C}}_{\it{T}} + \frac{{\it{\lambda }}}{2}{\it{\delta }}^{\it{2}}\), \({\it{\lambda }}_1^3 = - {\it{(f}} + {\it{g}} - \frac{{\it{\lambda }}}{2}{\it{\delta }}^{\it{2}}{\it{)}}\)

E₂(0, 0, 0)

\({\it{\lambda }}_2^1 = {\it{a}}\), \({\it{\lambda }}_2^2 = - {\it{C}}_{\it{T}}\), \({\it{\lambda }}_2^3 = {\it{f}} + {\it{g}} - \frac{{\it{\lambda }}}{2}{\it{\delta }}^{\it{2}}\)

E₃(0, 1, 1)

\({\it{\lambda }}_3^1 = {\it{a}} - {\it{b}}\), \({\it{\lambda }}_3^2 = {\it{C}}_{\it{T}} - {\it{d}} - \frac{{\it{\lambda }}}{{\it{2}}}{\it{\delta }}^{\it{2}}\), \({\it{\lambda }}_3^3 = - {\it{(f}} + {\it{g)}}\)

E₄(0, 1, 1)

\({\it{\lambda }}_4^1 = {\it{a}}\), \({\it{\lambda }}_4^2 = {\it{C}}_{\it{T}}\), \({\it{\lambda }}_4^3 = {\it{f}} + {\it{g}}\)

E₅(1, 0, 1)

\({\it{\lambda }}_5^1 = - {\it{(a}} - {\it{b)}}\), \({\it{\lambda }}_5^2 = {\it{c}} + {\it{d}} - {\it{C}}_{\it{T}} + \frac{{\it{\lambda }}}{2}{\it{\delta }}^2\), \({\it{\lambda }}_5^3 = - {\it{(e}} + {\it{f}} + {\it{g}} - \frac{{\it{\lambda }}}{2}{\it{\delta }}^2{\it{)}}\)

E₆(1, 0, 0)

\({\it{\lambda }}_6^1 = - {\it{a}}\), \({\it{\lambda }}_6^2 = {\it{c}} - {\it{C}}_{\it{T}}\), \({\it{\lambda }}_6^3 = {\it{e}} + {\it{f}} + {\it{g}} - \frac{{\it{\lambda }}}{2}{\it{\delta }}^2\)

E₇(1, 1, 0)

\({\it{\lambda }}_7^1 = - {\it{a}}\), \({\it{\lambda }}_{\it{7}}^{\it{2}} = {\it{C}}_{\it{T}} - {\it{c}}\), \({\it{\lambda }}_7^3 = {\it{e}} + {\it{f}} + {\it{g}}\)

E₈(1, 1, 1)

\({\it{\lambda }}_8^1 = - {\it{(a}} - {\it{b)}}\), \({\it{\lambda }}_8^2 = {\it{C}}_{\it{T}} - {\it{c}} - {\it{d}} - \frac{{\it{\lambda }}}{2}{\it{\delta }}^2\), \({\it{\lambda }}_8^3 = - {\it{(e}} + {\it{f}} + {\it{g)}}\)

E₉, E₁₀, E₁₁, E₁₂

At least one eigenvalue is greater than zero.