Simulink-Based Analysis for Coupled Metabolic Systems

Table 4

Stability analysis for the three biological systems. The independent variables in the branch pathway is set at = 0.6 (Case 1), 0.3 (Case 2), and 0.9 (Case 3). The independent variable in the cascade pathway is set at = 0.75 (Case 1), 0.9 (Case 2), and 0.6 (Case 3). The independent variables in the small-scale network are set at (x₆, x₇, x₈) = (1, 0.75, 0.75) for Case 1, (1, 1, 1.25) for Case 2, and (1.25, 1.25, 1.25) for Case 3.

	cases
	a branch pathway (4-gene)		A cascade pathway (3-gene)		A small-scale network (5-gene)
		stable		stable		stable
1	-1.0599 ±1.7013i	yes	-0.5543	yes	-13.0199	yes
	-7.9502 ± 1.6192i		-1.6468		-15.0341
			-4.6200		-26.6061
					-16.5117 ± 11.5849i
2	-1.2373±1.9465i	yes	-0.4818	yes	-14.9535	yes
	-9.7292 ± 1.0894i		-1.4313		-14.9535
			-4.0154		-29.9070
					-20 ± 14.1421i
3	-0.9651 ± 1.5704i	yes	-0.6581	yes	-17.3520	yes
	-7.1134 ± 1.5568i		-1.9552		-15.5201
			-5.4851		-25.7730
					-21.9829 ± 15.4717i