Table 2 Equilibrium point stability... | Emerald Publishing

Table 2

Equilibrium point stability evaluation

Equilibrium point	Eigenvalue	Sign	Stability condition
$E_{1} (0, 0, 0)$	$\begin{array}{l} λ_{1} = - A + n + f \\ λ_{2} = - H + D - T < 0 \\ λ_{3} = - K - e + L < 0 \end{array}$	$(○, -, -)$	Uncertain point; Stable for $A > n + f$
$E_{2} (1, 0, 0)$	$\begin{array}{l} λ_{1} = A - n - f \\ λ_{2} = - H + D - T + Q + n \\ λ_{3} = - K - e + L + P + f \end{array}$	$(○, ○, ○)$	Uncertain point; Stable for $A < n + f, H > D - T + Q + n, K > L - e + P + f$
$E_{3} (0, 1, 0)$	$\begin{array}{l} λ_{1} = - B + f - Q \\ λ_{2} = H - D + T > 0 \\ λ_{3} = - K < 0 \end{array}$	$(○, +, -)$	Saddle point
$E_{4} (0, 0, 1)$	$\begin{array}{l} λ_{1} = - A + n - P \\ λ_{2} = - H < 0 \\ λ_{3} = K + e - L > 0 \end{array}$	$(○, -, +)$	Saddle point
$E_{5} (1, 1, 0)$	$\begin{array}{l} λ_{1} = B + Q - f \\ λ_{2} = H - D + T - Q - n \\ λ_{3} = - K + P + f \end{array}$	$(○, ○, ○)$	Uncertain point; Stable for $B < f - Q, H < D - T + Q + n, K > P + f$
$E_{6} (1, 0, 1)$	$\begin{array}{l} λ_{1} = A + P - n \\ λ_{2} = - H + Q + n \\ λ_{3} = K + e - L - P - f \end{array}$	$(○, ○, ○)$	Uncertain point; Stable for $A < n - P, H > Q + n, K < L - e + P + f$
$E_{7} (0, 1, 1)$	$\begin{array}{l} λ_{1} = - B - P - Q \\ λ_{2} = H > 0 \\ λ_{3} = K > 0 \end{array}$	$(○, +, +)$	Saddle point
$E_{8} (1, 1, 1)$	$\begin{array}{l} λ_{1} = B + Q + P \\ λ_{2} = H - Q - n \\ λ_{3} = K - P - f \end{array}$	$(○, ○, ○)$	Uncertain point; Stable for $B < - Q - P, H < Q + n, K < P + f$

Note(s): + for positive sign; − for negative sign; unknown signs marked $○$