Qualitative stability of nonlinear networked systems
  In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions. 
Marco Tulio Angulo and Jean-Jacques Slotine
cs.SY math.OC physics.bio-ph