Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 87

that was formulated by Cohen and Grossberg (1983). In the above equation, IJ is the
time constant and x is the external input to the unit i . Solving this equation and
defining the network equilibrium state for the unit k of the network

h wv x ,

¦

k kj j k

j

the network should relax and ultimately reach the value y . Thereafter, the weights

k

are updated using the gradient descent method by

' wv g h D () y ,

lk l k k

where v h are the equilibrium values of unit l and the equilibrium net input

to the unit k respectively, and

and

l k

y is the equilibrium value of the matrix inverse

unit .

Z -1

Z -1

Z -1

Outputs

Z -1

Inputs

X 1 ( t n+1 )

y ( t n )

Bias

X 1 ( t n )

X 2 ( t n+1 )

Bias

X 2 ( t n )

X 3 ( t n+1 )

Bias

Figure 3.8. Fully connected recurrent neural network

A particular type of recurrent networks that do not obey the restrictions of the
Hopfield networks are the dynamic recurrent networks , proposed for
representation of systems whose internal state changes with time. They are
particularly appropriate for modelling of nonlinear dynamic systems, generally
defined by the state-space equations

X ( k +1) = f ( x ( k ), u ( k ))
Y ( k ) = Cx ( k ).