Information Technology Reference
In-Depth Information
4.5 Reaction-Diffusion Information Processing Devices
Distributed (continuous and discrete) systems represent one of the most important
types of natural objects, possessing high complexity of behavior and capable of
focused action. It is these systems that have attracted attention in recent years as a
promising basis for the establishment of efficient biologically motivated informa-
tion processing tools. In this case, processing of information occurs at every point of
the physical environment, which leads to a high degree of parallelism not compa-
rable with the possibilities of parallel computing by digital discrete processors.
The dynamics of distributed environments is described by systems of differential
equations giving the local changes in concentrations of the medium components
(
u
i
) during the evolution of the system in space and time:
X
u
i
∂
t
¼
∂
F
i
u
1
,
u
2
,
u
3
...
ð
u
N
Þ þ
D
ij
Δ
u
j
:
j
u
N
) describe the local dynamics of the inter-
action between the components of the medium, and the second term on the right
corresponds to the diffusion of its components.
In the state space corresponding to a reaction-diffusion system, basins of
attractors appear, i.e., certain dynamic regimes in which the system spontaneously
comes over into a stationary state. However, this movement within the basin does
not lead to qualitative changes of dynamics, i.e., to transition to another regime
(another attractor's basin). This can be defined as a dynamic redundancy in the
system. Therefore, there exists a fundamental possibility to create on the basis of
reaction-diffusion media devices that are capable, within certain limits, of chang-
ing their functions under the influence of external factors, i.e., possessing the ability
to learn.
The equations become considerably simpler in the case of continuous complete
intermixing of the components of the system. Due to the uniform distribution of the
components of the environment, diffusion mechanisms do not play any role, and the
dynamics is determined solely by the mechanisms of interaction between the
components:
Here, the functions
F
i
(
u
1
,
u
2
,
u
3
...
u
i
∂
∂
t
¼
F
i
u
1
,
u
2
,
u
3
...
ð
u
N
Þ:
The media described by such systems of equations are called the reaction-
diffusion media. Modes of operation of reaction-diffusion media are determined
by the function
F
i
(
u
1
,
u
2
,
u
3
...
u
N
). From the standpoint of information processing,
the most interesting media are those with nonlinear mechanisms of interaction
between components. They demonstrate a high complexity of behavior and carry
out basic operations of information processing that are logically complex actions,
