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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.
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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