By G. Palm, R. Heim (auth.), Roland Heim, Günther Palm (eds.)
Read or Download Theoretical Approaches to Complex Systems: Proceedings, Tübingen, June 11–12, 1977 PDF
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Additional resources for Theoretical Approaches to Complex Systems: Proceedings, Tübingen, June 11–12, 1977
Example text
State space description of the system (cf. section 1). Let us assume that some properties of the asymptotic behaviour of a particular system are expected on heuristic grounds - a situation that may arise in two different ways: 1) The behaviour of the system has been observed thoroughly for a long time. 2) The system has been designed to achieve a certain goal asymptotically. Then one may try to translate these heuristic ideas into·a mathematical language in order to use them as an additional tool in a general asymptotic analysis of the system.
Toog ~ 9 implies (Toog, 11) ~ L) = o. e. I(Qplp) J ~I(pli:» J J J J for every p £X: J I(Qplp) - I(plp) =k. (Qp). ) -k. ) J J JJ ~~ ~~ =k. (L::. Q .. ) -k. p. (k. Q .. ) = J ~ ~ ~J J J ~ ~ J ~J ~ ~ = k ij Pi Qij • log ( (Qp)j Pi/ (Pi Pj» ;!! k ij PiQij«QP)jPi/(Pi Pj) -1) = = l:j (k i PiQij) (Qp)j /P j - k ij Pi Qij = kj (Qp)j - 1 = O. 3) In (2) equality holds iff (Qp). /(p. p~) = 1 for all i,j , J ~ J • which implies Pi/P i = 1 for all i. 'l'hus for p '" P we have 9 (Qp)