discrete time steps

set of real numbers

x i ( t )

ith internal state variable at t


number of the Gaussian maps in the coupled network

w i j

symmetric auto-associative matrix


number of the stored patterns

α , β , and ε

system parameters of the Gaussian associative memory

ξ i k

ith pixel of kth input binary pattern with a discrete value of zero or one

h i

correction coefficient corresponding to ith classified group


( x 1 , x 2 , , x 16 ) Τ

x *

fixed point of function f


( f 1 , f 2 , , f 16 ) Τ

D f

Jacobian matrix of function f


characteristic multipliers or eigenvalues of D f


16 × 16 Identity matrix

E u

intersection of 16 and the direct sum of the generalized eigenspaces of D f ( x * )

L u

D f ( x * ) | E u

0 D

completely stable fixed point

k D , k > 0

“directly” unstable fixed point

k I , k > 0

“inversely” unstable fixed point

P1, P2, P3, and P4

stored patterns with 10 × 10 pixels

Pr1, Pr2, Pr3, and Pr4

reduced patterns of stored patterns with 4 × 4 pixels

G l m

tangent bifurcation of m-periodic point

I l m

period-doubling bifurcation of m-periodic point