Let . Then at any stationary state,
s at 0 can be discarded from the rest of the analysis. It will be shown below that if the stationary state is stable, at most one can be at the lower solution of equation 2 (inequality 5). Suppose that there is such an (if there is not, a stronger inequality is derived, see Appendix B), and let be such that . It will be shown below that any steady state where is unstable, and we can therefore suppose . Then
Consider the right-hand side of the above inequality as a function of . It is an increasing function, and for the above inequality to hold, it must also hold for the maximum of that function (which is for ), where , ie
This implies in particular , where is the number of non-zero s, generalizing the result obtained by Cinquin (2005).