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We consider the problem of counting (stable) equilibriums of an importantfamily of algebraic differential equations modeling multistable biologicalregulatory systems. The problem can be solved, in principle, using realquantifier elimination algorithms, in particular real root classificationalgorithms. However, it is well known that they can handle only very smallcases due to the enormous computing time requirements. In this paper, wepresent a special algorithm which is much more efficient than the generalmethods. Its efficiency comes from the exploitation of certain interestingstructures of the family of differential equations.

Special Algorithm for Stability Analysis of Multistable Biological Regulatory Systems