. 2023 Apr 6;24:136. doi: 10.1186/s12859-023-05206-2

Table 2.

Summary of parameter perturbation rules

Condition	Stabilize	De-stabilize	Parameter cluster for $S S_{2}$
${\hat{m}}_{ij} < 0$	Decrease k $↓$	Increase k $↑$	${k_{3}, k_{4}}$
${\hat{m}}_{ij} > 0$	Increase k $↑$	Decrease k $↓$	${k_{1}, k_{2}}$

Condition	Increase	Decrease	Parameter cluster
	separation	separation	for switch
${\hat{s}}_{j} < 0$	Decrease k $↓$	Increase k $↑$	${k_{3}, k_{4}}$
${\hat{s}}_{j} > 0$	Increase k $↑$	Decrease k $↓$	${k_{1}, k_{2}}$

Enumeration of parameter perturbation directions to: (i) stabilize or de-stabilize a given stable state (based on the sign of ${\hat{m}}_{ij}$ ) and (ii) increase or decrease the separation between stable states (based on the sign of ${\hat{s}}_{j}$ ). Parameter clusters corresponding to the stated conditions are also listed. Note that the trends for clusters based on both sensitivities are similar. The symbol $↑$ indicates an increase in the stability property listed for that column and $↓$ indicates the decrease thereof