Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria - Advancing Artificial Intelligence Through Biological Process Applications - page 353

Figure 13. The time evolution of the state's components for the neural network with the delays t 1 = 0.3
sec, t 2 = 0.1 sec, t 3 = 0.3 sec

of frequency domain inequalities combined with
some comparison principle. The results have been
encouraging and stimulating for new development
of the standard Lyapunov theory. In fact the main
conclusion of the chapter points out the necessary
development of the mathematical instrument in
parallel to the technological growth here and
elsewhere.

circumstances, new specific structures (with
“emergent computing capabilities”, to cite Hop-
field) will presumably appear. Consequently,
science and technology will deal with new struc-
tures of various physical natures having multiple
equilibria. At least the following qualitative
behaviors will remain under study: stability-like
properties (dichotomy, gradient behavior a.s.o.),
synchronization (forced oscillations, almost linear
behavior, chaos control) and complex dynamics
(including chaotic behavior). Such kinds of dy-
namic behavior - at least some of them - have
been discussed here. We consider that each new
dynamical structure with multiple equilibria will
bring its specific features to be discussed within
the qualitative theory.
Under the circumstances one has to foresee the
development of the mathematical instrument. The
main tool will remain, as presumable, the method
of the Lyapunov function whose applications to
the stability and oscillations is but well known.
Actually we have to remark here the viability of
several paradigms that underline this contribu-
tion as well as many other (some being cited in
the references). One of them is that sub-symbolic
AI systems are modeled by dynamical systems
with several equilibria having adequate dynami-

FUTURE TRENDS

The content, as well as the approaches of the pres-
ent contribution, is a frontier one from the point
of view of Artificial Intelligence development. At
the same time the field tackled here has its own
dynamics and trends, which are “ignited” by fac-
tors that may be independent of AI. We should
thus analyze the trends of the theory of systems
with several equilibria independently but also in
connection with the field of AI.
Supposing the field of AI has its own dynam-
ics, one has to admit that the neural networks and
their structures will evolve in order to improve
the imitative behavior i.e. more of the “natural”
intelligence will be transferred to AI. Under the