Considered is a class of n-dimensional dynamical systems
where the matrix is symmetric and the system as a whole is competitive. Several examples of applications of this type of equations are indicated as nonlinear neural networks and, in general, global pattern formation.
A global Lyapunov function for the system discussed is introduced. Its absolute stability with infinite but totally disconnected equilibrium points is studied by the LaSalle invariance principle. Decomposition of equilibria of the system into suprathreshold and subthreshold variables is also presented is called suprathreshold at t if where stands for inhibitory threshold of .