Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria - Advancing Artificial Intelligence Through Biological Process Applications - page 352

Figure 11. The time evolution of the state's components for the delayless neural network

Figure 12. The time evolution of the state's components for the neural network with admissible delays
for preserving the asymptotical stability t 1 = 0.003 sec, t 2 = 0.001 sec, t 3 = 0.2 sec

It is mentioned first that design and training
of this devices is somehow independent of the
necessary dynamical properties (in the sense that
the networks are designed and trained for other
purpose than, e.g., to ensure their own qualita-
tive capabilities). From here the necessity of the
dynamics studies as some kind of a posteriori
analysis. This analysis uses all achievements
and results of the theory of dynamical systems

with several equilibria and globally Lipschitz
nonlinearities.
These systems have in most cases an associated
“natural” Lyapunov function. This fact allowed
obtaining sufficient (but natural) conditions of a
“good behavior” for the neural networks viewed
as dynamical systems. This theory is less devel-
oped for systems with time delays; for this reason
there was applied the technique of V. M. Popov