Fig. 1
From: Using sensitivity analyses to understand bistable system behavior
The smallest bistable chemical system proposed by Wilhelm [41]. In this work, we applied eigenvalue and steady state separation sensitivity analyses on this system. (a) Chemical reactions where species concentrations [X] and [Y] are considered to be the two states of the system. (b) Reaction rate equations where x and y are the time-dependent states of the system. The reaction rate constants \(k_1\), \(k_2\), \(k_3\), and \(k_4\) are non-dimensional. (c) x- and y-nullclines of the system, showing the two stable steady states (blue markers) and saddle node (red marker) at the points of intersection. (d) One-parameter bifurcation diagrams (or S-curves) corresponding to parameters \(k_1\) through \(k_4\). The width of the S-curve for each parameter represents the bistable region. (See Additional file 1 for more details of the system)