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Table 2 Summary of parameter perturbation rules

From: Using sensitivity analyses to understand bistable system behavior

Condition

Stabilize

De-stabilize

Parameter cluster for \(SS_2\)

\({\hat{m}}_{ij} < 0\)

Decrease k \(\downarrow \)

Increase k \(\uparrow \)

\(\{k_3,k_4\}\)

\({\hat{m}}_{ij} > 0\)

Increase k \(\uparrow \)

Decrease k \(\downarrow \)

\(\{k_1,k_2\}\)

Condition

Increase

Decrease

Parameter cluster

 

separation

separation

for switch

\({\hat{s}}_{j} < 0\)

Decrease k \(\downarrow \)

Increase k \(\uparrow \)

\(\{k_3,k_4\}\)

\({\hat{s}}_{j} > 0\)

Increase k \(\uparrow \)

Decrease k \(\downarrow \)

\(\{k_1,k_2\}\)

  1. 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 \(\uparrow \) indicates an increase in the stability property listed for that column and \(\downarrow \) indicates the decrease thereof