Using sensitivity analyses to understand bistable system behavior

BMC Bioinformatics

Table 1 Summary of eigenvalue analysis on the simplest bistable system [41]

	Solution 1	Solution 2	Solution 3
Steady States (x, y)	(0,0)	(2, 0.5)	(6, 4.5)
Jacobian \(\textbf{J}\)	\(\left( \begin{matrix} -1.5 &{} 16\\ 0 &{} -8 \end{matrix}\right) \)	\(\left( \begin{matrix} -6 &{} 14\\ 4 &{} -8 \end{matrix}\right) \)	\(\left( \begin{matrix} -18 &{} 10\\ 12 &{} -8 \end{matrix}\right) \)
Eigenvalues \((\lambda _1, \lambda _2)\)	\((-1.5,-8)\)	\((-14.5,0.54)\)	\((-25.04,-0.95)\)
Stability Property	Stable	Saddle node	Stable

For each steady state solution, the corresponding Jacobian, eigenvalues, and stability are listed. There are two stable steady states, which make this system bistable

ISSN: 1471-2105