Ecoinformatics Problems in the Future World - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 818

a b

(3) s a and s b types of active elements the m-th type having m

m and

m

m elements

and:

X

s a
m¼1 m

X

s b
m¼1 m

a b

m ¼ D a ð 0 Þ; m ¼ D b ð 0 Þ;

ð 10 : 5 Þ

respectively.
In the discrete case, the change of the average number of system elements that
have survived till the moment ti+1 i+1 will be described by the following relations:

;

n

hs ð t i Þ p hs ð t i Þ

H s ð t i þ 1 Þ ¼max 0 ; H s ð t i Þr s ¼ 1 ; ... ; m h ; ð 10 : 6 Þ

n o

;

n

Rj ð t i Þ p Rj ð t i Þ

a j ð t i þ 1 Þ ¼max 0 ; a j ð t i Þr j ¼ 1 ; ... ; r h ð 10 : 7 Þ

;

h h n

Cm ð t i Þ p Cm ð t i Þ

m

m ð t i þ 1 Þ ¼max 0

; m

m ð t i Þr

m ¼ 1 ; ... ; s h ð 10 : 8 Þ

;

h

nl ð t i Þ p nl ð t i Þ

N l ð t i þ 1 Þ ¼max 0 ; N l ð t i Þr l ¼ 1 ; ... ; m n ð 10 : 9 Þ

;

h

Rs ð t i Þ p Rs ð t i Þ

b s ð t i þ 1 Þ ¼max 0 ; b s ð t i Þr s ¼ 1 ; ... ; r n ð 10 : 10 Þ

;

m ð t i þ 1 Þ ¼max 0 m ð t i Þr Cm ð t i Þ p Cm ð t i Þ

m ; m m ¼ 1 ; ... ; s h ð 10 : 11 Þ

a ð b Þ
x i

r ð t Þ values characterize the external behavior of both these systems:

where the

g ;

; r g; ; r

H ð i e ¼ f r N ð i e ¼ f r

a
bl

a
Rs

b
as

b
Rj

and p a ð b Þ

x i ð t Þ are the respective probabilities of death of the elements as a result of
their interaction.
The following limiting conditions should be taken into account here:

X

Cs ð t i Þ p Cs ð t i Þþ X bj ð t i Þþ X Rj ð t i Þþ X

T
i¼0 fr

m b
j¼1 r

r b
j¼1 r

s b
j¼1 r

b a a a

Cj ð t i Þg ¼ m

h
l ð 0 Þ;

ð 10 : 12 Þ

X

Cs ð t i Þ p Cs ð t i Þþ X aj ð t i Þþ X Rj ð t i Þþ X

T
i¼0 fr

m a
j¼1 r

r a s a

j¼1 r

a b b b

Cj ð t i Þg ¼ m

n
l ð 0 Þ;

r ð 10 : 13 Þ

j¼ !