Journal of Robotics, Networking and Artificial Life, Vol. 1, No. 1 (June 2014), 73-79

The Recollection Characteristics of Generalized MCNN Using Different Control Methods
Shun Watanabe, Takashi Kuremoto*, Shingo Mabu, Masanao Obayashi

Graduate School of Science and Engineering, Yamaguchi University
Ube, Yamaguchi, 755-8611, Japan
E-mail: {s005we, wu, mabu, m.obayas}@yamaguchi-u.ac.jp
Kunikazu Kobayashi

School of Information Science and Technology, Aichi Prefectural University
Nagakute, Aichi, 480-1198, Japan
E-mail: kobayashi@ist.aichi-pu.ac.jp*

Corresponding author. E-mail: wu@yamaguchi-u.ac.jp
Tel: +81-836-85-9520

Abstract
Kuremoto et al. proposed a multi-layer chaotic neural network (MCNN) combined multiple Adachi et al.'s CNNs torealize mutual auto-association of plural time series patterns. However, the MCNN was limited in a two-layer
model. In this paper, we extend the MCNN to be a general form (GMCNN) with more layers and use particle
swarm optimization (PSO) to improve the recollection performance of GMCNN. The recollecting characteristics bydifferent parameter-control methods were investigated by computer simulations.
Keywords: chaotic neural network, association memory, time-series pattern, particle swarm optimization.

1. Introduction
Hopfield model has characteristics of a transfer of
network energy to a stable state and an ability torecollect a stored pattern stably1. On other hand, achaotic neural network (CNN) proposed by Aihara et al.
is able to recollect multiple stored patterns dynamicallybecause CNN consists of neurons which internal states
perform unstably and chaotically2.3. Generally, chaotic
neural network models proposed in the 1990s are known
as their recollection characteristics of “chaotic
itinerancy”, which means stored patterns are recollected
one by one in aperiodic states2-4. CNNs are applied to

not only dynamic association memory3 but also
optimization5 and complex computing6. Additionally,
Kuremoto et al. have combined multiple CNNs to be amulti-layer chaotic neural network (MCNN)7-11. MCNN
is able to recollect mutually multiple time series patterns
by controlling the unstable behaviors of CNN. Control
methods for MCNN are proposed by various
approaches, e.g., by observing the amount of dynamical
state changes9,10, or upper and lower limit of recalling
times12,13, and meta-heuristics (e.g., genetic algorithm,
particle swarm optimization (PSO))14. MCNN has been
applied to a mathematical model of hippocampus torealize a transform of long-term memory8-11. However,

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S.Watanabe, T. Kuremoto, S. Mabu, M. Obayashi and K. Kobayashi

in these works, the number of layers in MCNN was
limited to two layers. So we modified MCNN to be a
generalized MCNN (GMCNN) and have investigatedrecollect characteristics of GMCNN using direct control
method (DC)15. However, characteristics of GMCNN
using other control methods was not investigated andcompared.
In this paper, a meta-heuristics control method using
PSO (PSOC) for GMCNN was proposed.
Computational simulations of 2, 3, and 4 layers
GMCNN were reported and the recollection
characteristics of GMCNNs using DC15 and PSOC werecompared by the simulation results.

each other and play either role of "display layer" or"association layer". "display layer" means a state of thelayer keeps static. "association layer" means the layer
output patterns dynamically. GMCNN is able torecollect multiple time series patterns by switching theroles between CNN layers. The dynamics of the chaotic
neuron of CNN layer in GMCNN is defined as follows:N i n (t  1)  k1 n  i n (t )   wijn, n x jn (t )j 1

 i n (t  1)  k 2n  i n (t )  k 3 n x i n (t )  a i n
M

 i n (t  1)  k 4n  i n (t )    wijn , m x jm (t )n(b)Fig. 1 Association memory models: (a) a chaotic neural
2,3
network (CNN) , (b) a generalized multi-layer chaotic neuralnetwork (GMCNN)7-11.

2. Association Memory ModelIn this section, a generalized multi-layer chaotic neuralnetwork (GMCNN) which consists of plural chaotic
neural networks (CNNs)7-11 of Aihara et al. and its
storage/recollection methods of multiple time series
patterns are introduced.
2.1. Generalized Multi-layer Chaotic Neural Network
GMCNN is structured by interconnecting chaotic
neurons of CNN layers which have same network
structures15. In Fig.1 (a), a CNN is shown and in Fig.1(b) a GMCNN which has multiple CNN layers is shown.
The chaotic neurons in CNN layer connect to each otheras complete connected recurrent network as same as
Hopfield network1. CNN layers in Fig.1 (b) connect ton f y (t  1)n
xi (t  1)   i n
 xi (t )Outputs ofanother CNN

Outputsm  n j 1ny i (t  1)   i (t  1)   i (t  1)   i (t  1)

External inputs

Outputs(a)External inputs

(1)

N

n

n

 if R (t ) ,n(2)otherwise

where, t is an association time, n, m  1,, M  is
CNN layer number, i, j  1, , N  is neuron numberof CNN layer, M is the number of CNN layers in
GMCNN, N is the number of the neurons of one CNN
layer,  i n (t ),  i n (t ),  i n (t ) are internal states for
feedback inputs from self-layer, refractoriness andinputs from another layers respectively, wij n, m  is aconnection weight from j th neuron of m th layer toi th neuron of n th layer, k1 n , k 2n , k 4n are decay
parameters for feedback inputs from self-layer,
refractoriness and inputs from another layersnrespectively, k 3 is a refractory scaling parameter,nai is a summation of threshold and external input, nis a rate of effectiveness from another layers, y i (t ) isnnnan internal state, x  {x1 (t ),, x N (t )} is an output ofnCNN, R (t ) is a propositional function ( n th CNNnlayer performs as "association layer" if R (t ) isfulfilled, otherwise the layer performs as "display
layer"). f () is a output function of the neuron:f ( y) 1
1  e y (3)where,  is a steepness parameter. k n  {k1 n ,, k 4n }are called internal parameters in this paper.
2.2. Storage Process of Time Series Patterns

GMCNN stores each partial pattern of plural time series
patterns into the multiple CNN layers alternately.
Hebbian learning rule16 for storing the plural time series
patterns are defined as follows:

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The Recollection Characteristics of GMCNNg t l   t l mod M  1
t l   M  t l  m  1   m  1
M





 

 

 ij t l ,  m t l    2  i t l   1  2  j  m t l   1
0n,m
t l   0
 w ij  t ,  m t 
ij
l
l

n ,m

if





wij

if

n,m

 wij

n  g t l  ,n  mi  j,otherwisen,m wijt l 

(5)where, t l is a storage time, χ tl   {1 tl ,,  N tl } is apartial pattern of the time series patterns at tl , g tl  ism
the layer number to store a pattern,  t l  is a storage
time for m th layer at tl ,  is floor function,  is an ,mstorage rate, wij tl  is a correction mass of theweight, Eq.(5) is an equation to renew state at tl .
2.3. Network Energy

GMCNN has a characteristic of transfer network energy(NE) to a local minimal state when the network outputs
its stored pattern (also called "recollection")1 because
GMCNN store the patterns by Hebbian learning rule(which is also used in Hopfield network1, CNN2,3, andMCNN8-11). In this paper, the equation of NE is defined
as a follow:
E (t )  

1 ifz i (t )  
0

(4)

m

1 M M N N n,m n wij xi (t ) x jm (t )2 n1 m1 i 1 j 1

(6)

3. Control Methods

The meta-heuristics control method using PSO (PSOC)
is proposed for controlling the state of each CNN layerand switching the roles of “display layer” and“association layer” for GMCNN. The controlled thenparameter of CNN layer are k . The propositionalnfunction R (t ) of Eq.(5) is defined as n  n' (t ) inorder to make only one CNN layer as “association
layer” at all times. n' (t ) is the layer number as“association layer” at time t and is defined a follow:
n' (t ) mod M  1 if Q(t )n' (t  1)  n' (t )
otherwise(8)

The direct control method (DC)15 controls“association layer” in GMCNN by switching then '( t )internal parameters k
to different parameters fromthe amount of decrease of state changes of the layer.
However, the switching parameters were set arbitrarily.
In this paper, optimal parameters are found by a metaheuristic method described in the next subsection andthey are used to “association layer” to control the layer.
3.1. Particle Swarm Optimization Control Method (PSO)

Particle swarm optimization (PSO) is a meta-heuristic
method base on an exploratory behavior of a group of
birds or fishes proposed by Kennedy and Eberhart17,18.
An exploration of optimal parameters by PSO is run
according to a joint ownership parameter in a search
space. Here, PSO is used to find the optimal parametersof each CNN layer in GMCNN. In Refs.14, Kuremoto
et al. used PSO to find the optimal parameters of
MCNN, however, to evaluate fitness of each particle, it
is used stored patterns during recalling process. To
eliminate this supposition, the stability of NE given by
Eq.(6) can be used to evaluate the fitness of eachparticle. An algorithm for the control method using PSO
named “PSOC" is shown as follow:[Algorithm for PSOC]
Step 1 Initializations of the particles are defined asfollows:
s0
min
max
u pd ( s )  U u d , u dv ( s )  U v
pd

min
max
, vd
d




(9)

n '(t )

Step 2 x(t  1) is calculated by Eq. (1)-(2) usingn '(t )kgiven by u p (s ) . The fitness of p th particle isdefined as follows:(7)

where, Q(t ) is a propositional function for switching
the role of CNN layer to be “display layer” or“association layer” at time t . The output of GMCNN
for observing the output of “association layer” isdefined as a follow:n '( t )(t )  0.5
xi
otherwiseE t , u p ( s )  E (t )  E (t  1) k n '( t ) u ( s )



 



F u p ( s )  max E t , u p ( s ) ,0

(10)

p

Step 3 Equations for renewing the particles are defined
as follows:v pd ( s  1)  u pd ( s )  c1 r1 uˆ pd ( s )  u pd ( s ) c r u~ ( s )  u ( s )
2 2

d

pd

u pd ( s  1)  u pd ( s )  v pd ( s  1)

Step 4 The particles are reevaluated by Eq.(10).

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(11)

S.Watanabe, T. Kuremoto, S. Mabu, M. Obayashi and K. Kobayashi

Step 5 This process is repeated from Step 3 if anmax
iteration step s fulfills s  s. Otherwise, thisprocess ends and “association layer” is renewed by Eq.
~ ( s ) is applied to k n '(t )(1)-(2) ( t  t  1 ) after u~(s) ). Q (t ) of Eq. (7) is defined as E(t )  E(t  1) .
( k n'(t) u
where, U (a, b) is an uniform random number in a rangeminmax[ a, b] , u d
and u dare the minimum value andthe maximum value in a d -dimensional rangeminmax, v pd (s ) is a velocity of d  1,, D th
ud , udparameter of p  1,  , P th particle at step s ,E (t  1) k n '( t ) u is the NE of Eq.(6) in “associationplayer” renewed by Eq.(1)-(2) in a case that parametersu p ( s )  u p1 ( s ),, u pD ( s ) of p th particle at step sn '( t )of the layer at time t , F u p ( s ) isare applied to k
the fitness of p th particle,  is an inertia coefficient,
c1 , c2 are coefficients for local and global search, r1 , r2
are uniform random numbers in a range [0,1] ,~~~uˆ p ( s )  uˆ p1 ( s ),  , uˆ pD ( s ) and u ( s)  u1 ( s),, u D ( s) are thebest parameters in all past of p th particles and allparticles and defined as follows:

















uˆ p ( s )  arg max F u p ( s ' )u p ( s ') 0 s ' s

~ ( s )  arg max F uˆ ( s )upu p ( s ) 0 p  P



(12)

In this section, the storage / recollection simulations of
GMCNN using DC15 and PSOC and their results arereported. The neurons of all CNN layers are stimulatednby the external input ai in each simulation. And
recollections of partial patterns of time series patterns
are observed as the output of GMCNN. The external
input is defined as a follow:n ce 2 ˆ i  1

(13)

where, ce is a scaling coefficient for external input,χˆ  ˆ1 , , ˆ N  is an external input pattern given toeach CNN layer.
Table 1 shows parameter setting in all simulations.
Table 2 shows parameter setting in 3 kind of thesimulation environments: Env.1 with 2 CNN layers,
Env.2 with 3 CNN layers and Env.3 with 4 CNN layers.
In this paper, the number of kinds of the time series
patterns stored in GMCNN is 2 defined as follows:r (0,1) if 0  t l  4χ (t l )  r (0,1) if 7  t l  11
 0.5
otherwiseSymbolInitial internal states i (0),  i (0),  i (0)0Initial connection
weight

n ,m
ij

w

0

Initial patterns

n

(14)

Value

Random pattern



0.015

100

N
n

n

n

x i ( 0)

Steepness parameter
Dimension ofparameters
Number of particle
Maximum step

Search velocity
range

D

4

P

10
20

max

s

Search space range{1,1,20,1}

u

max

u

min

{0,0,0,0}v

max{1,1,20,1}v

minc1 , c 2{-1,-1,-20,-1}
1
1n ' ( 0)1Inertia coefficient
Search coefficients
Initial association
layer

Table 2 Parameter setting of each simulation environment.
The numberof layerM2
3
4

Environment
number

4. Computational Simulations

ai

Table 1 Parameters setting.
Name
Number of neurons
in a CNN

Env.1
Env.2
Env.3

Rate ofeffective ness

1
0.5
1/3

Learning
rate

Scalingcoefficient



ce

0.2
0.3
0.4

6
9
12

r (0,1) if 0  t l  4
r (0,1) if 7  t  11l
χ (t l )  
r (0,1) if 4  t l  18
 0.5otherwise(15)

where, r (0,1) is a binary pattern randomized with 0 or
1, χ tl   0.5 means no pattern can be observed(because  ij tl , m tl  in Eq. (4)). Eq. (14) gives 2 timeseries patterns ( 0  tl  4 , 7  tl  11 ) which areconsisted of 5 random binary patterns. An interval
between these time series patterns are 2 from storage
time tl  5 to tl  6 . On the other hand, Eq.(15) gives 3
time series patterns consisted of 5 random binary
patterns which intervals between these time series
patterns are 2 respectively ( tl  5,6 , tl  12,13 ).
In computational simulations, recollection processesof the stored plural time series patterns were observed
from t  1 to t  100 in Env.1-Env.3 and in GMCNNs
using DC15 and PSOC. The recollection processes wererepeated 100 times (as 100 samples) to evaluate a

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



The Recollection Characteristics of GMCNN

performance of GMCNN by each average stored pattern
retrieval times in Env.1-Env.3.

( χ 0 ,, χ 3 , χ 7 ,, χ 10 and a non-stored random
pattern).
In Table 3, above data in cells mean the average
retrieval times, and under data in parentheses are
deviations.

(a) DC(a) A case of 2 time series patterns in Eq.(13) for a 2-layer
GMCNN (Env.1)(b) PSOC
Fig. 2 Examples of GMCNNs which stored the times series
patterns of Eq. (14) in Env.2 and given χ (2) of Eq. (14) asexternal input.

Fig. 2 shows storage processes and recollection
processes of GMCNN with 3-CNN layers (Env.2). The
plural time series patterns stored in GMCNN is thepatterns of Eq. (14). Fig. 2 (a) is using DC. Fig. 2 (b) isusing PSOC. The external input to GMCNN was arandom pattern as same as the stored pattern at thestorage time tl  2 given by Eq. (14).
The left column of Fig.2 (a)-(b) shows the storage
processes of GMCNN for storing 2 time series patternχ 0 ,  , χ 11 of Eq.(14) by Eq.(4)-(5). The rightcolumn of Fig.2 (a)-(b) shows the recollections of thestored patterns ( χ 0 ,  , χ 4  and χ 7 ,  , χ 11 ) on an
above ten lines and the role of “association layer” on anunder three lines in GMCNN with 3-CNN layers fromthe association time t  1 to t  100 . From Fig.2, we
can confirm that the switching of roles of CNNs worked
constantly and χ 2  , χ 3 and χ 4  were recollected indifferent association times. And PSOC resulted morerole switching times of 3-CNN layers than DC,
comparing the role switching times of DC and PSOC (↓in Fig.2).
To investigate the relationship between the external
input and the output of GMCNN (retrieval patterns), on
columns in Table 3, we show the average retrieval
frequencies of 10 stored patterns ( χ 0 ,, χ 4 andχ 7 ,, χ 11 ) in GMCNNs with Env.2 given
respective 9 kinds of the external input patterns(b) The case of 2 time series patterns in Eq.(13) for a 3-layer
GMCNN (Env.2) in Table 3(c) A case of 2 time series patterns in Eq.(13) for a 4-layer
GMCNN (Env.3)(d) A case of 3 time series patterns in Eq.(14) for a 2-layer
GMCNN (Env.1)(e) A case of 3 time series patterns in Eq.(14) for a 3-layer
GMCNN (Env.2)(f) A case of 3 time series patterns in Eq.(14) for a 4-layer
GMCNN (Env.3)
Fig. 3 The average total retrieval frequencies, the average total
switching frequencies and the expectancies of GMCNNs (foran association time from t=1 to 100 in 100 samples) given bydifferent parameter control methods: DC and PSOC; “ ★ ”
denotes that over one of total retrieval, total switching and“expectancy” in the GMCNN using PSOC are higher than in
one using DC.

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S.Watanabe, T. Kuremoto, S. Mabu, M. Obayashi and K. Kobayashi

Table 3 The average retrieval frequencies of the part of thestored time series patterns, the average of their totals, theaverage total switching frequencies and the expectancies of
the number of the patterns recollected for an association
time from t=1 to 100 (and their standard deviations) in
GMCNN which store Eq. (14) in Env.2 (in 100 sample).
Storedpatternχ ( 0)χ (1)χ ( 2)χ (3)χ ( 4)
χ ( 7)χ (8)χ (9 )

χ (10)
χ (11)(a) DC
External input pattern: χ̂χ ( 0)χ (1)χ ( 2)

18.89(2.15)
6.22(4.28)
31.56(6.19)
0.00(0.00)
0.13(0.93)
0.00(0.00)
0.00(0.00)
0.00(0.00)
0.00(0.00)
0.00(0.00)

0.00(0.00)
20.31(5.81)
19.66(8.51)
20.63(5.09)
0.89(1.56)
0.00(0.00)
0.00(0.00)
0.00(0.00)
0.00(0.00)
0.00(0.00)

0.00
0.00
0.00
(0.00) (0.00) (0.00)
0.00
0.00
0.00
(0.00) (0.00) (0.00)
0.26
0.00
23.50
(8.61) (2.59) (0.00)
0.00
16.75 28.75(9.95) (8.71) (0.00)
0.00
17.82 22.62(7.01) (13.88) (0.00)
0.00
0.00
21.92
(0.00) (0.00) (5.08)
0.00
0.00
5.88
(0.00) (0.00) (4.39)
0.00
0.00
24.73
(0.00) (0.00) (6.05)
0.09
0.06
0.02
(0.90) (0.42) (0.20)
0.85
0.43
0.26
(3.93) (2.54) (1.02)

χ (3)

χ ( 7)

χ (10 )

random

0.00
0.00
0.05
(0.00) (0.00) (0.50)
0.00
0.00
0.00
(0.00) (0.00) (0.00)
0.00
0.00
0.00
(0.00) (0.00) (0.00)
0.09
0.00
0.38
(0.63) (0.00) (2.35)
0.10
0.00
0.09
(0.70) (0.00) (0.63)
0.00
0.00
0.00
(0.00) (0.00) (0.00)
0.00
0.00
22.54
(7.39) (0.00) (0.00)
0.00
12.96 17.43(7.41) (1.80) (0.00)
13.87 24.27 28.70(5.49) (11.57) (8.34)
1.26
29.30 22.97(2.07) (3.56) (14.46)

0.00(0.00)
0.01(0.10)
0.61(1.77)
1.29(2.58)
1.68(3.51)
0.00(0.00)
0.00(0.00)
0.50(2.63)
0.39(1.60)
2.70(5.20)χ (8)χ (9 )

Total
56.80 61.49 59.01 52.12 52.81 50.82 71.00 52.19
7.18
retrieval (8.46) (12.31) (17.39) (20.34) (11.30) (14.38) (11.81) (19.70) (8.71)
Total
34.07 26.15 28.06 32.98 32.31 26.30 29.30 32.93 23.11
switching (3.51) (3.29) (3.46) (4.43) (3.22) (3.21) (3.22) (4.40) (3.67)
3
3
2
3
3
3
2
0
expectancy 3(b) PSOCStoredExternal input pattern: χ̂pattern χ (0) χ (1) χ ( 2) χ (3) χ (7) χ (8) χ (9) χ (10) randomχ ( 0)χ (1)χ ( 2)χ (3)χ ( 4)
χ ( 7)χ (8)χ (9 )

χ (10)
χ (11)

13.82(6.70)
13.14(7.60)
21.72(2.31)
9.97(6.53)
7.49(6.29)
0.00(0.00)
0.00(0.00)
0.00(0.00)
0.01(0.10)
0.00(0.00)

0.25
0.22
0.00
(0.90) (0.70) (0.00)
0.33
0.00
14.56
(6.97) (1.00) (0.00)
17.29 17.51 13.19(7.71) (9.79) (10.83)
17.40 15.74 22.94(7.54) (10.00) (6.20)
6.71
15.68 20.39(5.60) (9.82) (7.11)
0.00
0.00
0.00
(0.00) (0.00) (0.00)
0.00
0.02
0.20
(0.00) (0.20) (1.32)
1.08
3.27
0.52
(3.67) (6.96) (2.55)
1.22
3.24
0.63
(3.99) (6.95) (2.84)
1.24
3.42
1.46
(4.02) (7.12) (3.98)

0.22(0.61)
0.15(0.74)
1.56(4.82)
1.89(4.97)
1.70(4.61)
4.93(3.19)
3.68(3.18)
16.59(7.18)
13.55(6.65)
12.79(6.45)

0.14(0.79)
0.29(0.98)
1.38(4.39)
1.90(4.78)
1.69(4.45)
0.04(0.31)
8.61(6.40)
14.39(8.26)
14.63(8.34)
8.18(7.05)

0.00
0.38
0.45
(0.00) (1.14) (1.27)
0.00
0.33
0.65
(0.00) (1.11) (1.67)
0.12
3.73
5.18
(1.19) (7.31) (8.55)
0.15
4.69
5.57
(1.49) (7.87) (8.39)
0.12
4.00
5.20
(1.19) (7.41) (8.28)
0.00
0.00
0.00
(0.00) (0.00) (0.00)
0.00
0.00
0.11
(0.00) (0.00) (0.82)
8.63
4.29
26.88
(3.13) (10.03) (7.98)
4.38
25.88 14.14(3.24) (10.03) (8.12)
4.67
26.10 12.53(3.26) (10.18) (8.42)

Total
66.15 59.75 59.43 59.33 57.06 51.25 79.25 48.43 30.50
retrieval (10.98) (21.49) (24.16) (20.26) (17.61) (23.35) (6.27) (26.10) (29.43)
Total
62.87 62.66 65.94 64.43 59.13 60.29 73.83 61.37 58.12
switching (5.39) (5.48) (6.09) (6.27) (4.93) (5.24) (4.97) (6.19) (5.73)
4
3
3
5
4
3
2
0
expectancy 5

The bold number in Table 3 means the average
retrieval frequency is larger than its deviation (that is
the recollection of the stored pattern is expected and it iscalled “expectancy” in this paper). Height of the“expectancy” indicates higher recollection performanceof GMCNN. GMCNN using PSOC showed higher

expectancy, comparing GMCNNs using DC in Table
3(a) and PSOC in Table 3(b).
Total retrieval frequencies of all stored patterns,
total switching frequencies and expectancies for eachexternal input pattern in Table 3 and other simulations
are illustrated in Fig. 3. Fig. 3 (a) is in a case of 2 timeseries patterns given by Eq. (14) in 2-layer GMCNN(Env.1). Fig. 3 (b) and (c) is in 3-layer GMCNN and in
4-layer GMCNN. Fig. 3 (d)-(f) is in a case of 3 timeseries patterns given by Eq. (15) in 2, 3 and 4-layer
GMCNN.
The better performance of GMCNN using PSOC
than DC (marked with ★) is concluded, comparing thetotal retrieval frequencies, total switching frequencies
and expectancies in respective external input patterns.
Therefore, PSOC proposed in this paper is suggested
preferentially as the control method of the switching therole of CNN layers as “display layer” and “association”
in GMCNN.
5. Conclusion
In this paper, we proposed the control method using
PSO as meta-heuristics which finds and uses the optimal
parameters in GMCNN. In the computational
simulations using 3 kinds of parameter setting, 2 kindsof time series patterns, different external input patterns
and 2 kinds of the control methods (DC and PSOC), thebetter performance of GMCNN using PSOC wasconfirmed by comparing the processing results of DC
and PSOC. The highest expectancy is in 3-layer
GMCNN. As future works, GMCNN is expected to be
adopted into long term memory models and the limbic
model of the brain.
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