Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria - Advancing Artificial Intelligence Through Biological Process Applications - page 354

cal properties to ensure correct operation. The
other one, which is borrowed from the theory
of Hamiltonian and gradient systems, is that a
“natural” Lyapunov function is associated to
define structures of systems (Halanay & Răsvan,
1993; Răsvan, 1998). The other methods i.e. the
frequency domain inequality Popov type and the
comparison principles are useful substitutes for
those cases where the Lyapunov function(al) is
not available. Even in such cases we should ex-
pect development of the Lyapunov method since
the Popov like inequalities are of matrix type for
systems with several nonlinear functions - the
case of AI devices, in particular of the neural
networks.
From this point of view we hopefully consider
that involvement of new mathematical develop-
ment will bring new qualitative results for the
dynamical systems of AI e.g. in the case of systems
with time delays.

sary to discuss more about the method of V. L.
Kharitonov of constructing Lyapunov functionals
for time delay systems. One may find here the
old idea of stating from a given derivative for the
Lyapunov functional in order to reach via a suit-
able and not very abstract construction, a good
Lyapunov functional satisfying suitable estimates
ensuring the required qualitative behavior. The
Kharitonov-like constructions for various types
of delay equations and various behaviors define
an interesting research direction. It appears that
such research could be rewarding in both fields
of dynamical systems and AI devices.

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FUTURE RESEARCH DIRECTIONS

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The interaction of the two paradigms - emergent
capabilities of neural networks and gradient-like
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able dynamic behavior for normal operation of this
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making use of sharper inequalities. The research-
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procedures and results of the Lyapunov methods,
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