Biomedical Engineering Reference
In-Depth Information
Chapter XVIII
Dynamics of Neural Networks
as Nonlinear Systems with
Several Equilibria
Daniela Danciu
University of Craiova, Romania
AbSTRACT
Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one
is concerned with what we would call “learning dynamics”. The second one is the intrinsic dynamics of
the neural network viewed as a dynamical system after the weights have been established via learning.
The chapter deals with the second kind of dynamics. More precisely, since the emergent computational
capabilities of a recurrent neural network can be achieved provided it has suitable dynamical proper-
ties when viewed as a system with several equilibria, the chapter deals with those qualitative properties
connected to the achievement of such dynamical properties as global asymptotics and gradient-like
behavior. In the case of the neural networks with delays, these aspects are reformulated in accordance
with the state of the art of the theory of time delay dynamical systems.
INTRODUCTION
simple computing element is here the neuron or,
more precisely, the artificial neuron - a simplified
model of the biological neuron.
Artificial Neural Networks structures are
broadly classified into two main classes: recurrent
and non-recurrent networks. We shall focus on
the class of
recurrent neural networks
(RNN).
Due to the cyclic interconnections between the
neurons, RNNs are dynamical nonlinear systems
displaying some very rich temporal and spatial
Neural networks are computing devices for
Ar-
tificial Intelligence
(AI) belonging to the class of
learning machines (with the special mention that
learning is viewed at the sub-symbolic level). The
basic feature of the neural networks is the intercon-
nection of some simple computing elements in a
very dense network and this gives the so-called
collective emergent computing capabilities
. The
Search WWH ::
Custom Search