. 2023 Mar 29;9(4):e14982. doi: 10.1016/j.heliyon.2023.e14982

Table 3.

The eigenvalues of each equilibrium point corresponding to the Jacobi matrix.

Equilibrium points	Eigenvalue $λ_{1}$	Eigenvalue $λ_{2}$	Eigenvalue $λ_{3}$
$E_{1} (0,0,0)$	$(1 - k) R_{G} - C_{G} + 2 T$	$R_{A 1} + R_{A 2} - C_{A}$	$R_{B 1} + R_{B 2} - C_{B}$
$E_{2} (0,0,1)$	$(1 - k) R_{G} - C_{G} - C_{G B} + T$	$R_{A 1} (α + 1) + R_{A 2} (β + 1) - (1 - γ) c_{A}$	$- ({R_{B}}_{1} + R_{B 2} - C_{B})$
$E_{3} (0,1,0)$	$(1 - k) R_{G} - C_{G} - C_{G A} + T$	$- ({R_{A}}_{1} + {R_{A}}_{2} - C_{A})$	$R_{B 1} (α + 1) + R_{B 2} (β + 1) - (1 - γ) c_{B}$
$E_{4} (0,1,1)$	$(1 - k) R_{G} - C_{G} - C_{G A} - C_{G B}$	$- [R_{A 1} (α + 1) + R_{A 2} (β + 1) - (1 - γ) c_{A}]$	$- [R_{B 1} (α + 1) + R_{B 2} (β + 1) - (1 - γ) c_{B}]$
$E_{5} (1,0,0)$	$- [(1 - k) R_{G} - C_{G} + 2 T]$	$R_{A 1} + R_{A 2} + C_{G A} - C_{A} + T$	$R_{B 1} + R_{B 2} + C_{G B} - C_{B} + T$
$E_{6} (1,0,1)$	$- [(1 - k) R_{G} - C_{G} - C_{G B} + T]$	$R_{A 1} (α + 1) + R_{A 2} (β + 1) - (1 - γ) c_{A} + C_{G A} + T$	$- (R_{B 1} + R_{B 2} + C_{G B} - C_{B} + T)$
$E_{7} (1,1,0)$	$- [(1 - k) R_{G} - C_{G} - C_{G A} + T]$	$- (R_{A 1} + R_{A 2} + C_{G A} - C_{A} + T)$	$R_{B 1} (α + 1) + R_{B 2} (β + 1) - (1 - γ) c_{B} + C_{G B} + T$
$E_{8} (1,1,1)$	$- [(1 - k) R_{G} - C_{G} - C_{G A} - C_{G B}]$	$- [R_{A 1} (α + 1) + R_{A 2} (β + 1) - (1 - γ) c_{A} + C_{G A} + T]$	$- [R_{B 1} (α + 1) + R_{B 2} (β + 1) - (1 - γ) c_{B} + C_{G B} + T]$