Portland State University. Systems Science Ph. D. Program
Term of Graduation
Date of Publication
Doctor of Philosophy (Ph.D.) in Systems Science
System theory, Isomorphisms (Mathematics), Stochastic systems, Mathematical sociology, Psychology -- Mathematical models, Markov processes
1 online resource (vii, 149 pages)
The identification of isomorphisms between disparate systems is an important focus of systems science. Such isomorphisms have not only conceptual and pedagogical value to systems science, but they also provide pragmatic value to specific disciplines by suggesting new ways to model familiar phenomena and by serving as reference models that show how even simple models can generate complex behavior. Specifically, this dissertation looks at certain classes of stochastic dynamic systems (SDS) and shows that similar equations can model phenomena in sociology and psychology. In both disciplines, what is modeled by these SDS isomorphisms is a certain type of reliability, defined as the satisfaction of constraints, expressed in terms of first passage (exit) times to boundaries.
In mathematical sociology, the work revisits older literature on Markov models of occupational mobility and generalizes it to show how SDS can model intra-generational mobility and escape from poverty traps. By looking at exit-times and exit-probabilities of escape from such traps, it points out features of social dynamics, such as transients, which are often missed by equilibrium macroeconomic and macro-sociological models.
In mathematical psychology, the work looks at literature on drift-diffusion models (DDM) of time constrained judgment and decision making. Inspired by models of escape from attractor and stochastic switching dynamics in simple neurophysiological processes, it proposes extensions of DDM, again illustrating the role of exit-times and exit-probabilities. These models could serve as null reference models for experiments in cognitive psychology and motivate new experiments.
From the highly biology-centered systems science perspective, the probability distribution (and its moments) of the first exit out of a region in state space has a natural biosemiotic interpretation in terms of viability or lack thereof. Potential applications to modeling biological behavior are also sketched in this work. The SDS approach connects with Ashby's law of requisite variety, Simon's concept of satisficing, and Holling's dynamic systems idea of resilience. Thus in addition to offering new ways to model phenomena in the social sciences and biology and suggesting new mathematical and scientific questions worth pursuing, the models developed in the dissertation add to the repertoire of significant systems isomorphisms, continuing the tradition of Ashby's Introduction to Cybernetics and Zwick's forthcoming Elements and Relations.
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Venkatachalapathy, Rajesh, "Systems Isomorphisms in Stochastic Dynamic Systems" (2019). Dissertations and Theses. Paper 5410.