"NEUROLOCATOR", A MODEL OF ATTENTION 
V.I. Kryukov 
Research Computer Centre, 
LISSR Acaclemy of Scienc:es 
Pushchino, Moscow Region, 142292 
USSR 
ABSTRACT 
A most important consequence of our theory of 
phase tr'ansitions in the brain {Kryukov et al  
1986]. is the prediction that CNS contains a 
phase-lockecl trac:king system for controlling 
attention and memory in the frequency range of 
alpha- and theta-- rhythms. This paper describes a 
simplified model of such a system and discusses a 
basic: integro-cliffer'ential equation for its 
functioning which is almost identical to the 
ecluation for the well-known in communication 
phase-locked loop (PLL) .Dynamical properties of 
this system are sl-or't].y disc:ussecl to account for 
the experimental data which are difficult to 
interpret in terms of the existing moclels. 
THE PROBLEM OF ATTENTION 
By attention we mean a psychophysiological 
consisting simultaneously of two components, namely 
and synthesis. The first c:omponent is taking one of 
simultaneously possible objects or trains of 
process 
nalysis 
several 
thought. 
Foc:alization and concentration are of its 
closesst analogy is a searchlight {Crick, 1984}. 
component is a process of c:ombining several 
features (modalities) into single object. The 
Tr ei s!arl ...... 
analogy is a glue   , Gelade, 1o} 
The major problem of modelling attention is usually 
essence. The 
The second 
clistinct 
simplest 
thought 
as follows: if a model obtainss mixed signals from 
different sources, it should be able to recognize any 
component of the mixture. But most difficult part of the 
problem is probably a moda;ity and submodality integration. 
Papers conc:erned with modelling attention are st11 
relatively few {Crick 1984; Fukushima, I986; Grossberg, 
  ,86. They are all connectionism' 
1,8; Malsburg, Schneider, 
eurolocatoF', A Model of Attention 611 
None of them makes e,,,'plicit use of the following ideas which 
we believe crucial for understanding the functic:n of 
attention. 
1. The main functional element is the model 
a group of nonformal neurons {Kirillov et 
Kovalenko et al. 1.984; Kryukov et al., 1.986; 
1984}., which, being repeated in slightly 
and combinations, serves as a single 
system model of attention. 
2. During active perception of external 
modules and the whole of the system work 
of an assembly, 
al, 1989, 1986; 
Kryukov, 1982, 
different versions 
submodule for the 
sti mul i, separate 
near points of an 
unstable equilibr'ium resembling the physic:al effect of 
acta. stability of phase transitions and we think that this 
property reflects really existing phase transitions in the 
brai n. 
.7. The key principle of integration of modules into a system 
is the A.A. Uk'htomskii dominant prin.ciple which d...o..termines 
the entire functioning of the brain {Ukhtomskii, 1978}. We 
associate it in an explicit manner with phase transitions, 
low-frequency EEG oscillations and phase locking of these 
oscillations .Kryukov et al, 1986}. 
MINIMAl. MODEL.. OF THE SYSTEM 
1. The system model consists of the following six major 
subsystems (see Figure 1A): a septal oscillator (SO), a 
type of voltage controlled oscillator, as described in 
{Kryukov et al, 1986}; M independent cortical oscillators 
(CO) described in {K. irillov et al, 1988; Kryukov el' al, 
1986}; a phase detector (PD) of hippocampal field CA...-.., 
{Kryukov et al, 1986} a loop filter (LF) of midbrain 
reticular formation; an input mixer (IM) of hippocampal 
fascia dentara; and an output mixer (OM) of lateral sept urn. 
2. Each subsystem is 
model {Kryukov et 
e"citatory neurons 
subsystem and with 
subsystem output. The 
supposed to be fixed 
in all the neurons si 
a small modification of basic neuronal 
al, 1986} with some proportion of 
receiving inputs from the preceding 
an inhibitory neuron acting as the 
thresholds of inhibitory neurons are 
but those of the excitatory ones vary 
mu!taneously by the value pr'opcrtional 
to current nonspecific activation (arousal). 
..'.?,. All CO"s have sensory inputs , each of particular 
submodality, being thereby independent stimulus feature 
analysers. Their (fixed) thresholds are distributed among 
different CO's so that their mean frequencies are 
distributed uniformly in t. he alpha--theta freq. enc:y band. 
612 Kryukov 
CO' s 
A 
IM 
PD 
OM 
LF 
SO 
VC 
NC 
( FD+CA 5 ) S 1 RF S m 
FD+Cj) 
VC 
Figure 1. Schematic diagrams of the "Neurolocator" (A) and 
its neurobiological counterpart (B). PD = phase detector., /.F 
= loop filter, VC = voluntary control, CO = cortical 
oscillator., SO = septal oscillator, IM = input mixer., 
outp_!t mixer, NC = neocortex., FD = fascia dentata. 
field of the hippocampus., RF = reticular formation, 
medial septurn and S 1 = lateral septurn. 
OM = 
CA.. = 
S m = 
4-. PD has two major inputs - septal and neocortical. The 
septal input is supposed to be of fi;,'ed amplitude , that is 
"Neurolocator", A Model of Attention 613 
of the fixed degree of bursting, but the neocortical input 
has a variable amplitude A =(B Ai)/M where A i is the degree 
of bursting of the i-th input (to IM) which is dependent on 
the arousal. 
5. LF has transfer function F(p) =: K/(I+Tp) (Sinc:e K acts on 
the system like A, we identify AK as a single parameter 
measuring the arousal.) 
6. The main assumption is that the (focus) attention can be 
operationally described as n collective property of the PLL 
cotrol system emerging at some value of the model 
parameters. This property corresponds to phase locking or 
pulling together of the fr'e:quencies of many otherwise 
independent CO's as the result of system synchronization at 
dominant frequency. 
Figure 1A shows a structure similar to that of a radar' range 
tracking system which may well account for the origin of the 
term "Neurolocator" {Kryukov, loo. Despite a rather 
complex structure of the model it can be shown theft the 
joint spike activity of output neurons of CO's and SO form 
a Markov system and can be described by the same Kholmogorov 
equation as the basic model activity {Kryukov, 1984}. 
Therefore considering the following analog of the mean 
activity of the system ('relative phase') 
M 
_. 
of distribution of !(t) for large M. Namely, if F(p)=K then 
8 :-U t / 8 2 () 
BUt/St = [o- AKg(1)] 8Ut/SI + (D(B)/M) 2 
where g(]!) is some nonlinear function such that g(O) = 8 and 
max g() = 1. The constant o means an average of initial 
deviation (detuning) of the CO's frequencies from the 
frequency of SO. 
MAIN PROPERTIES AND/OR PREDICTIONS OF THE "NELIROLOCATOR" 
1. Attention is impossible when arousal is low. For a small 
gain (AK < qo ) the system develops either' chaotic activity 
or' beating oscillations with periods equal to 
 2) 
T b = 2  ( 1' ( . -1/2 
-- .AK)  ' 
2. Attention arises when arousal exceeds a threshold value. 
614 Kryukov 
Actually, when AK > lo, the system locks the !hase of SO to 
the phase of dominant group of CO"s. The system exhibits 
attention also in a sense that it gives preference to some 
frequency and, thereby, to extern.l and internal signals 
initiating and supporting the oscillations. At this time all 
other signals produce incoherent activity, which means 
almost the same as if they did not exist at all for the 
system. 
.]. Attention is selective and can be controlled. By varying 
flo, we can tune SO to some or other frequency of CO "picking 
out" particular signals from mixture of signals. Usually, 
frequency is set automatically (unconsciously), after which 
the tracking starts, i.e. the phase of SO becomes 
automatically adjusted to the mean phase of CO's. The time 
of frequency and phase setting may be identified with the 
reaction time or recognition time. !t will correspond to the 
time needed for the system to pass frown ..r unstable state to 
one of the "stationary states". Its numercl esimmt:.s 
are, therefore, quite analogous to those given in {Kirillov 
et el, 1986} and should strongly depend on th i:i. tial phae 
and detuning. 
4. Attention is unstable or, at most, roetastable. Due to the 
noise (O()  8), each "stationary state" has a finite 
lifetime depending on the parameters and initial states of 
the system. 
5. Breakdown of attention may be abrupt (for example, due to 
"catching" of SO by another CO) or gradual. In the latter 
case the model shows an interesting nonlinear effect of 
cycle slipping.It can be described as j.mping of the phase 
difference between SO and CO to a value of : 2 so that SO 
can perform one oscillation more or less than the leading 
CO. 
6. As arousal increases, attention is growing i.e. phase 
tracking gets more precise, but only to c certain threshold 
value, after whic:h attention drops anew. It car be shown 
that in the "Neurol ocator" the plot of a summar"y mean--squ.re 
error in phase tracking versus the gain AK is a U-shaped 
curve. For small AK dynamic errors are large,a. nd for large 
AK errors rise again due to noise and instability. 
7. Attention is unitary, but for some, intermediate level of 
arousal,it can be divisible . It is .ell known that two 
stimuli are perceived by the nervous system as different if 
the interval between them is greater than a threshold value 
, otherwise they will be perceived as one stimulus. We can 
show that the "Neurolocator" with many parallel inputs shown 
Neurolocator , A Model of Attention 615 
in Figure 
CO' s can 
note that 
equivalent to the following expression 
dB/dt = l o - [Ag(!;!) + N(t)] F(p) 
lB may exhibit such a synchronization that some 
have their own phases relatively SO. Let us first 
eq,_ation () with account of LF will be 
where N(t) is white noise. We can show that for the diagram 
in Figure lB the multichannel version of this equation is 
valid, i.e. 
M 
d!i/dt = loi- [ I] Aijg (;.) + N.(t)] F(p) i = 1. M () 
=I J    ' ' ' ' ' ' ' 
where Aij = crossintensity of i--th and j-th inputs. 
If thiq system has a steady-state solution {.i } then it 
will imply that CO's are phase-locked through the partial 
control of the common SO even if they initially do not 
directly interact. However, for large A i .K all E;i being 
tracking errors should decrease, and attend. ion should become 
unitary. We believe that this effect bears on a very small 
capacity of short-term memory at high arousal. In any case 
it agrees with the known e,xperimental facts on the divided 
attention .Kahneman, 197..}. 
CONCLUDING REMARKS 
The properties listed above are sLfficient for unified 
explanation of many psychological facts such as Cocktail - 
Party effect, Yerkes - Oodson law, Stroop effect {Kahneman, 
197.}, eature Integration effect {Treisman, Gelade, 198]-. 
The model provides invariant object recognition through 
analysis by the synthesis on time-division multiplexing 
basis. Phase-frequency-space coding is universal for all 
sensory modalities and is probably the same for thinking and 
moving. 
The model provides also simple explanation for many 
neurobio!ogical data such as EEG and ERP: SO drives COs in 
cyclical way and this results in composite scalp voltage 
emanating from CO's located at different distances from 
superf i ci al el ectr odes; ERP are nothi ng more but 
synchronized EEG transients. The wave P5.8 in particular is 
the sign of several model functions: CO's de!ayed 
the SO interrogation, memory reado..v, reset wave, 
PD, shifts of attention etc. 
The model can work as associative memory due to 
of equation () to usual Sejnosky- 
important difference is that here 
reply to 
mismatch of 
similarity 
Hopfield equation. The 
A i j means virtual 
616 Kryukov 
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That corresponds to the evidence that connections required 
for associative recall are formed not directly between the 
cortical areas in which the memories are stored but 
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