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Nonlinear Dynamics of Group Dynamics: Models from Mathematical Sociology. Barbara F. Meeker Professor Emerita Sociology Department University of Maryland College Park, MD SCTPLS Baltimore July 2012. Outline.
Barbara F. Meeker
University of Maryland
College Park, MD
SCTPLS Baltimore July 2012
Source: Lotka, 1932
O2,t = O2,t-1 + O2,t-1(-R2*O1.t-1 – S2*O2,t-1 + C2) (1.2)
This system is sensitive to values of the parameters:
R1*R2 < S1*S2 Convergence (2.1)
R1*R2 > S1*S2b Divergence (2.2)
"Computer Simulation for Exploring Theories: Models of Interpersonal Cooperation and Competition" R. K. Leik and B. F. Meeker Sociological Perspectives. 1995, 38:463-482. "Exploring Nonlinear Path Models via Computer Simulation" R. K. Leik and B. F. Meeker Social Science Computer Review 1996, 14:253-268. "Uses of Computer Simulation for Theory Construction: An Evolving Component of Sociological Research Programs" B. F. Meeker and R. K. Leik, Pp 47-70 in Status, Network and Structure: Theory Construction and Theory Development., edited by Jacek Szmatka, John Skvoretz and Joseph Berger; Stanford Univ. Press. 1997 "Some Philosophy of Science Problems in the Development of Complex Computer Simulations" chapter in The Growth of Social Knowledge: Theory, Simulation, and Empirical Research in Group Processes edited by Jacek Szmatka, Michael J. Lovaglia, and Kinga Wysienska, Praeger, Westport, CT 2002.
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Photos: B. Meeker
share .25 .25 .25 .25 Add 1 1 1 1
TopLo C=.5 1.0 .3 .2 r share .4 .2 .2 .2 Add 1 3 1 1
TopHi C=.5 .4 .3 .2
Share .40 .20 .20 .20:add 1 1 1 1
X2= 3.0000 R2=0.0500 S2=0.0700 C2=0.4000
X3= 3.0000 R3=0.0500 S3=0.0700 C3=0.3000
X4= 3.0000 R4=0.0500 s4=0.0700 C4=0.2000
R1Eq S1Eq C1Fix|R2Eq S2Eq C2Fix|R3Eq S3Eq C3Fix|R4Eq S4Eq C4Fix
Model is Interactive/OthersOutput is Current/No Delay/N= 4/Up,Dn half
fair share is 0.40 0.20 0.20 0.20
Add to Output #1 #2 #3 #4 1.00 3.00 1.00 1.00
Average total number of acts for each actor in the first 27 minutes of group
discussion by type of group.
Up (want to be ahead); if output is lower than standard, R or S decreases, hence Output increases. If output is higher than standard, R or S increases, hence Output decreases. DeltaUp[i] := rel[i,t] - share[i]
C = .5,.4,.3,.2 Share = .4,.2,.2,.2
Initial: start=3, r=.05, s=.07
R is ‘UP’,
S is ‘Fixed’
R and S