Ecoinformatics Problems in the Future World - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 816

A breach in stability of a system may result from internal causes (the aging of its
elements) or external causes associated with the unfavorable in uence of the envi-

ronment (an ill-intentioned enemy, in particular). Survivability of biological systems
is determined by environmental conditions where man

fl

is interference with nature is
one of the important factors. In connection with this and the prospects of constructing
arti

'

cial biological systems, optimization problems also arise; an increase of pro-
ductivity of a biological system being the main criterion of optimality.
For the global scale the problem of survivability of the interacting systems is
complicated at the expense of the hierarchy of interaction levels. For a complete
explanation of H and N systems their openness has to be taken into account. Com-
monly, let us consider the interaction of two open complex systems H and N,de ned

by their goals H G and N G, structures H S and N S and behavior H B and N B , respectively.
It is suggested that the functioning of such systems should be described by equations
of (V, W)-exchange. Namely, the interaction of an open system with the environment
(or other system) is represented as a process whereby the system exchanges a certain
quantity V of resources spent in exchange for a certain quantity W of resources
consumed. The aim of the systems is the most advantageous (V, W)-exchange, i.e. it
tries to get maximum W in exchange for minimum V. The V is a complex function of
the structure and behavior of both systems:

V ¼ VW ð ; H S ; N S ; H G ; N G Þ ¼ VW ð ; H ; N Þ ð 10 : 1 Þ

As a result of their interaction the systems H and N get the following (V, W)-
exchanges:

H N V H ; max ¼ V H ; max W H ; ð ; Þ ¼ max

H B ;

min
N B ;

V H ð W H ; H ; N Þ

f H S g f N S g

ð 10 : 2 Þ

H N

V N ; max ¼ V N ; max W N ; ð ; Þ ¼ max

N B ;

min
H B ;

V N ð W N ; H ; N Þ

f N S g f H S g

where H * and N * are the optimal systems H and N respectively.
From ( 10.1 ) and ( 10.2 ) one can see that the value of (V, W)-exchange depends
on the goal of the system and may vary within certain limits: V 1,min ≤ V H ≤ V 1,max ,
V 2,min ≤ V N ≤ V 2,max, where V i,min (i=1, 2) corresponds to the case, when both
systems are most aggressive, and V i,max (i = 1, 2) to the case, when they are most
cautious. In brief, there is some spectrum of the interactions between H and N. For a
formal description of these interactions we shall divide all the elements of both
systems into three classes: the working (working), protective (defensive) and active
elements, the latter designed to act on the environment. For short, we shall refer to
the working elements of systems H and N as a-and b-elements, to the protective
elements as R a -and R b -elements and to the active elements as C a -and C b -elements,
respectively.