Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://chronos.msu.ru/old/journal/files/archive/2005/02/13_levich_poisk.pdf Äàòà èçìåíåíèÿ: Sat Dec 14 12:37:05 2013 Äàòà èíäåêñèðîâàíèÿ: Fri Feb 28 20:55:47 2014 Êîäèðîâêà: Windows-1251 Ïîèñêîâûå ñëîâà: m 2

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. ..; Web- http://www.chronos. msu.ru; apl@chronos.msu.ru

. , "" , "" , - . . , , " ". ? . - . . , - - . , , " ". , : , ( ). , , . . " ", , . (, , -) . - . () . ( ) . : , , , . . , , .. . . - : , , . , .

: , , , , , .
*

( 05-06-80062).

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... 1. ? - , , , - ( - ). " ..." , . - , , - , . (. " ..." ). , - , . , , , , ... - , , . - . , ., ., , ... ., ,
1)

... -

, , (.. ) , . , - -, , . , -, , -. . . 2 (2), 2005. . 345-369 __________ 2 25


... , , , . , . ? , . , . - , . , . , , , , , . , " ", . : , , (, , 2004). XIX , - , . XX , , . , . , ( , ) (, 1960). "", , , "", . ., , , "" , "" (.. " ", "") . . . 2 (2), 2005. . 345-369 __________ 3 25


... , - . , - , , . : . "": , , . - - , . "" . , " " "", . , , . (Gzyl, 1995) . , , , , , , , , , .. . - - ( . (1985, . 93), " , , , , , "). - . , , . (Jaynes, 1957): 1. .

. . 2 (2), 2005. . 345-369 __________ 4 25


... 2. (, , ..). 3. . 60- , , , , . ? - , " ". - , ? , , , .

2. , " ", . - , , - , . , - . , , , . , . "" , . - - . . 2 (2), 2005. . 345-369 __________ 5 25


... . . , . (1963), - , . , , . , , ; ; - ; - ; - . - - . XX , , . - (, , 1972; , , 1974; , 1983; , 1986) - " " . , (, 1974; , , 1978; , 1982; ., 1990; Lequizamo n, 1993; Levich, So lov'yo v, 1999; , 2000). ( ) - . , , , . ? " " -

. . 2 (2), 2005. . 345-369 __________ 6 25


... , ? , , ( - ) . , , . , - "", "" . , (, , , , , ). .. XX . , . , ., ., . . . - . ., , ; " " .; ., ., .. .. . . , , . , . . 2 (2), 2005. . 345-369 __________ 7 25


... , . - , , . , . - , . - , , .. . - "" . , 2). - . - . - . , . . . : "" . "" ( (2004), "") : ( , ), . , " ", "" , "" . - , - " ".

. . 2 (2), 2005. . 345-369 __________ 8 25


... - , . - 3). , - , , ( ). , , , , . , , , - , .

3. - - , , - "-", "-" .. , -, - . , , "" ( "") , . " ". , " " (, 1982). , - . , ( - , ). . , . , , . " . . 2 (2), 2005. . 345-369 __________ 9 25


... ", " ", , "". , . . : ( ) - ? - , . - , , . , , , , , - . , , . , , . (), , " " (, 1982), " ", " ", ( ). , - . , , , , . , "" - " " - - , . "". . , . " ". . . 2 (2), 2005. . 345-369 __________ 10 25


... , , . . , . , - - . , , ( ). , , (, 1982). " ", - " ", " "4). , " " (, 2000). , "" , , . , , .. , , . ( ) . . : . , , (.. , ). , , . . 2 (2), 2005. . 345-369 __________ 11 25


... ( ) 5). , , , , , .. , .

4. , , . , "", - "". , , , . ( , , ) . ( , , .) . " " (: -, , ). , -, ( - , ) , -, , . , - . , . , - - . , . , , . . 2 (2), 2005. . 345-369 __________ 12 25


... , . .6). (, , ) . , "" . " " , " ". , ( - , . 2) , 7). : 1) . 2) , , (, "") . 3) , . 4) , .

5. . , , . , , (, 2007). , , - , , . (, "" . . 2 (2), 2005. . 345-369 __________ 13 25


... , (, 1996) .) , , . , , , , . ( , ) , , "" . , "" . "" , , . - , , , . : , , . , , , . - ( ). , , , " ". , . "" , (, 1980). . . , . . . . 2 (2), 2005. . 345-369 __________ 14 25


... - "" - - " " . " " . , , " " . ( ) . , . , , (, 2004). , , .

6. , : 1) ; 2) , , 3) . - . "" ( "") "", , " " (, 1996; 2007). . "-" , . , . . , "". . , , , . . 2 (2), 2005. . 345-369 __________ 15 25


... . ( ., 1994). "" , , .. , 8). : , , , , , , . , , - , , "" ( ), , "" , . , . , , (, , 2002). , , ( ) . : , ( ) , .

7. : 1) - . -

. . 2 (2), 2005. . 345-369 __________ 16 25


... . 2) , - - - . 3) , , " ". 4) , : , , ( ). 5) , , . . " ", , . (, , ) . - . () . ( ) . 6) : , , , . . , , .. 9). . 7) : . . 2 (2), 2005. . 345-369 __________ 17 25


... ž ž ž ž ; ("", "", " " ..); () , .. "" ; "" , " " ; ž ž ž ž ž . - . , , . - . , " ", . ž - , . , . 10): ž ž ž , . . . , .. , . 8) :

. . 2 (2), 2005. . 345-369 __________ 18 25


... ž . ( , . , , .) ž ž ž ž . 11). . - .


( ., 2003): (Lotka, 1922), "" (Odum, Pinkerton, 1955), (Ulanowicz, Han non, 1987; Schneider, Kay, 1994; Mauersberger, 1996), " " (Jørgensen, 1997), (Ulanowicz, 1986), (PérezEspaña, Arreguin-Sánchez, 1999), (Patten, 1986; 1995), (Margalef, 1968), (O'Neill et al., 1986), (Whittaker, Woodwell, 1971), (, 1980), " " (.., .., 1999). , - . "" , .. () , ( , , ) . , , . : , , "". " " . , , . , . , . , , . , , .
3) 2) 1)

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...
, () . . " ", "" . . , . . . , , . , , n !/ P ni ! , -
i
5) 4)

n , - , i ( , ). : ( ) . , , , ( - ).
6)

X A (Levich, 1995; 1996):

H (A)=
X

X

X I Q (A) % X I Q (A)

,

I Q (A) - X A Q , I Q (A) - X A %
X

% Q , Q , " ". . - .

H X (A) = log =

n nAÕ P ninAiX i

-n

X

å
i

niX n log iA , nX nA

niA niX - i A X ;

nA =

å
i

niA

nX =

å
i

niX - A X .
H X (A) = log n! . P ni !
i

- ,

- ,

H X (A) = log

2 n A nX = P 2 niAniX
i

nA nX ( 1 -

å
i

niA niX ). nA n X

- , - ni n . : (Tribus, 1961); "" , (Gell-Mann, 1994); -, (, 1996); (, 1997); (, 1998).
7)

. . 2 (2), 2005. . 345-369 __________ 20 25


...
, "" .. (Clausius, 1865), "" , , "". .
8)

:

H( L ) =

å
k
m

l k ( L )Lk .
- , l ( L)
k

H - , L ? L , L , ...L
1 2

{
K

}

- , L . , , :
w n n ì H ( n1 , n2 , ..., nw ) = -nå i log i R max ï n i =1 n ï w ï k k ïå qi ni ? L , k = 1, m; í i =1 ïw ïå ni = n; ï i =1 ïn ? 0, i = 1, w. îi

ni - i , w - qi - " " k i . (, , 2002), H

k

( ) . . , , , ( ). , , . . , , . .. , , . : ( "" ) , " " ( ) . , , , . , - . , " , " . ( , 1997; Levich, 2000; , 2004).
10) 9)

LK

? 0 , .. -

. . 2 (2), 2005. . 345-369 __________ 21 25


...
11)

( ., 1994):
m

Õ
k =1

m

Lk (-

) 2 - 1 (), "" . S , J ?Æ -- J

{1, 2, ..., m} , :

1) (. (8)) ni ( L ) , L ? L , L , ..., L
1 2

{

m

}

, -

L , k Î J (, ); 2)

k

å
i= 1

w

qik ni ? Lk

k Î J k Ï J qi .
k

.. . .: , 1974. 207. ., . . .: , 1972. 259. . // . .: , 1963. . 245-259. . . . .: , 1983. 488. .., .. // . 2004. 1. . 105-136. .. // . 1997. . 3-4. . 98-120. .. . : - . -, 2004. 364. .. . .: , 1986. 440. .., .., .. . .: . , 1990. 81. .., .. , : . .: , 1999. 320. .. . .: - . -, 1980. 180. .. , . .: - . -, 1982. 190.

. . 2 (2), 2005. . 345-369 __________ 22 25


... .. : // : . 1. . .: - . -, 1996. . 149-192. .. // , . .: . ... . 2. 2000. . 163-176. .. // . .: -, 2004. .167-190. .. // . 2004. .124. 6. . 3-21. .. : // : . 3. . . . . . 2007. .., .. // . 2002. . 8. 4. . 1035-1045. .., .., .. // . 1994. .6. 5. . 55-71. .., .., .. : . .: - , 1997. 192. ., . : . .: , 1978. 312. .. , . .: . 1960. 600. . . .: , 1985. 328c. .., .., .. // . 2003. . 123. 2. . 115- 137. .. . .: , 1998. 168c. .. . .: , 1996. 448 . .., .. . .: , 1974. 256. . . 2 (2), 2005. . 345-369 __________ 23 25


... CLAUSIUS R. Über verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie //Ann. Phys. Fo lge 2. 1865. Bd. 125. S. 353-400. GELL-MANN M. The quark and the jaguar: adventures in the simple and the co mplex. New York: W.H.Freeman, 1994. 392p. GZYL M. The method of maximum Entropy. Singapore, New Jersey, London, Hong Kong: World Scient ific, 1995. 146p. JAYNES E.T. Infor mational theory and statist ical mechanics // Phys. Rev. 1957. V.106. Pp. 620-630. JØRGENSEN S.E. Integration of Ecosyste m Theories: a Pattern 2nd.. Dordrecht: Kluwer, 1997. 400p. LEQUIZAMON C.A. The periodic continuous effect in terms of algebraic relation theory // Int. Journal of Bio logical Systems. 1993. V.1. No 1. LEVICH A.P. Time as variabilit y o f natural syst ems // On the Way to Underst anding the Time Pheno menon. Part 1. Singopore, New Jersey, London, Hong Kong: World Scientific, 1995. Pp. 149-192. LEVICH A.P. Variat ional modelling theorems and algocoenoses funct ioning principles // Ecological Modelling. 2000. V. 131. Pp. 207-227. LEVICH A.P., SOLOV'YOV A.V. Category-functor modeling of natural systems // Cybernet ics and Systems. 1999. V.30. No 6. Pp. 571-585. LOTKA A.J. Contribut ion to the energetics of evolut ion // Proc. Natl. Acad. Sci. 1922. N.8. Pp. 14 -150. MARGALEF R. Perspect ives in ecological theory. Chicago: Chicago Universit y Press,1968. 122p. MAUERSBERGER P. From a theory o f local processes in aquat ic ecosystems to a theory at the ecosystem scale // Sci. Total Environ. 1996. 183. Pp.99-106. ODUM H.T., PINKERTON R.C. Time's speed regulat or: the optimum efficiency for maximum power output in physical and bio logical syst ems // Am. Sci. 1955. 43. Pp. 331- 343. O'NEILL R.V., DEANGELIS D.I., WAIDE J.B., ALLEN T.F.H. A Hierarchical Concept of Ecosystems. Princeton, NJ: Princeto n Universit y Press, 1986. 392p. PATTEN B.C. Energy cycling, length of food chains, and direct versu s indirect effects in ecosystems // Ecosystem Theory for Bio logical Oceanography. Can. Bull. Fish. Aquat. Sci. 1986. 213. Pp. 119-138. PATTEN B.C. Net work int egrat ion o f eco logical extremal pr inciples: exergy, emergy, power, ascendency and indirect effects // Ecological modelling. 1995. 79. Pp. 75-84. . . 2 (2), 2005. . 345-369 __________ 24 25


... PÉREZ-ESPAÑA H., ARREGUIN-SÁNCHEZ F. A measure of ecosystem maturit y // Ecologocal Modelling. 1999. 119. Pp. 79-85. SCHNEIDER E.D., KAY J.J. Life as a manifestation of the second law of thermodynamics // Math. Comput. Model. 1994. 19. Pp. 25-48. TRIBUS M. Informat ion theory as the basic for thermostatics and thermodynamics //J. Appl. Mech. Ser. E. 1961. V.28. 1. Pp. 1-8. ULANOWICZ R.E. Growth and development: Ecosystems Phenomeno logy. N.Y.: Springer, 1986. 203p. ULANOWICZ R.E., HANNON B.M. Life and production o f entropy // Proc. R. Soc. Lond. 1987. 232. Pp. 181-192. WHITTAKER R.H., WOODWELL G.M. Evolution of natural co mmunit ies // Ecosystem Structure and Funct ion. Corvallis: Oregon State Universit y Press. 1971. Pp. 137-159.

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