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Introduction

The study of social processes has witnessed tremendous developments over the decades. Researchers, especially from the fields of sociology and Psychology, continue to present findings and evidence on the dynamics of different social phenomena (Julian, et al. 1995). Among the social phenomena that have been probed extensively include interpersonal and romantic relationships, engagement and marriage. However, there is a feeling that not so much work has been done on how scholastic modeling can be applied to social processes in attempt to explain the interconnections between different variables amongst the social phenomena under scrutiny.

Contemporary investigations give much emphasis on the continuous time models using individual data (Hadeler, 2010). Researchers, from both the field of sociology and discipline of Psychology, continue to work with variety of models using individual data in analyzing dynamic social processes. Actually, the dynamic social processes have become of great interest in almost all fields of sciences and social science. (Hadeler, 2010).

Leo‘s study applied scholastic modeling in studying the population growth of the sexes (Leo, 1968). The researchers utilized stochastic models in describing changes taking place in a sample numbers of men and women population in different age intervals within some period of time (Leo, 1968). Their first case of study was where either the numbers of females or males were marriage dominant. Their second case of study was where the numbers of neither males nor females in the different age intervals were marriage dominant (Leo, 1968). This study paved way for possible future investigations into the marriage social phenomena based on the scholastic modeling. Concomitantly, Forrester and Alfred focused on the dynamic modeling of the Arms Race. The study was centered on two models of engaged couples in tempestuous relationship (Forrester, & Alfred, 1985). Their study was exceptionally significant in the system dynamics introductory course applying the paradigm of scholastic modeling (Forrester, & Alfred, 1985). 

Hadeler investigated into the aspect of pair formation, in which case, a number of pair formation approaches were observed in multitype populations (Hadeler, 2010). This work attempted to address the classical two sex problem in much details based on the law of pair formation. It adapted a general approach to separation process and pair formation in studying one sex multitype population, and applied the same approach in studying two sex multitype populations (Hadeler, 2010). In trying to distinguish between the chosen and the choosing sex group, the study finds the ultimate model is symmetric, with a high probability for asymmetric in the rates of preference. Pair formation problem is then linked to the problem of connecting stochastic matrix to sub-stochastic matrix, so that probabilistic interpretation can be realized to the known formulas representation in pair distribution (Hadeler, 2010).

According to Wilhelm, “nonexistence or existence of exponentially persistent age distributions is determined by the vital rates of two sex population” (Wilhelm, 1994).  Wilhelm notes there has been a growing interest in the study of the dynamics of two sex populations, considering pair formation as the main reproduction step (Wilhelm, 1994).   The pair formation model is thus given great emphasis in the field of epidemiology and demography, especially when modeling sexually transmitted disease (ETDs) (Wilhelm, 1994).   Wilhelm posits that even though death and birth are generally assumed to be linear processes, pair formation models are useful nonlinear processes, given the fact that the very act of mating is nonlinear (Wilhelm, 1994).  

Carlos, Wenzhang and Jia formulated and analyzed a pair formation model for multiple groups baring arbitrary mixing probability and general rates of paring (Carlos, Wenzhang, & Jia, 1995). By using equal average durations for all relationships and assuming that the recruitment rates were constant, these researchers found that the dynamics were relatively simplified. This was due to the monopolistic features of dynamical systems linked with paring of heterogeneous population of females and males (Carlos, Wenzhang, & Jia, 1995).

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In examining matches between marriage couples, Linder (2003) used the structural approach. The structural approach was a two sided matching model which enabled the researcher to sort out the marital couples with regard to marriage market flexibility, utilizing the agent’s preference (Linda, 2003). The study found that for white men, education was less desirable in predicting marriage propensity as compared to wage. As for the black men, education was more desirable in predicting marriage ability compared to wage. It was also observed that there was more flexibility in the marriage market for the white men (Linda, 2003).

Catherine and Debra looked into the subjective processes in which the premarital partners became less or more committed to marriage with time (Catherine & Debra, 1997). This research identified two processes in commitment, that is, the relationship driven commitment process, and the event driven commitment process. It found that in the relationship driven commitment, there was smooth evolution of the commitment characterized by few reversals. In this instance, the partners in commitment process paid attention on factors such as their interactions, joint networks, activities that involved both of them and positive believes regarding the relationship. There were extreme variations in the event driven commitment. The event driven commitment process was coupled with massive downturns and sharp upturns. Partners in this commitment process focused on factors such as negative relationship believes, self disclosure, separate interaction in their social networks, conflicts, and negative network believes (Catherine & Debra, 1997). The researchers resolved that the partners in event driven relationships were less committed to marriage and were most likely incompatible. The partners in relationship driven process were more committed to marriage and were most likely compatible (Catherine & Debra, 1997).

This paper will be examining the extent to which scholastic models have been applied in modeling dynamic social processes. It follows the fact that different social processes can be investigated using the mathematical paradigms of scholastic modeling. There will be an extensive review of the previous literatures on the application of scholastic models in social phenomena. In the research conducted by Alessandria, Sergio and Gustavo, the social phenomena in focus was love dynamics, a problem that is know to reside in the filed of social Psychology (Alessandra, Sergio, Gustavo, 1997). Their study borrowed majorly from the attachment theory which they used in explaining the problem of romantic relationships. The researchers focused on the existence of cycle dynamics in romantic relations, arguing that the application of differential equation in modeling the dynamics of feelings was manifested in their cyclical love dynamics model (Alessandra, Sergio, Gustavo, 1997). This dissertation looks into how Alessandra, Sergio, Gustavo, (1997) utilized the mathematics paradigm in demonstrating how love dynamics can be stochastically modeled to further expound on the understanding of this social phenomena. It presents a comprehensive review on how scholastic modeling applies in romantic relationships, the case of cycle dynamics in romantic relations.

 The structure of this project would be as follows: Chapter one present the general overview on the use of scholastic models in studying dynamic social processes, including relationships, engagement and marriage.  It briefly reflects on how scholastic modeling has been applied in studying these social processes. Chapter two of this dissertation will be focused on the stochastic nonlinear dynamics of interpersonal and romantic relationships. Chapter three will investigate into the dynamic of marriage and engagement using a stochastic dynamic. 

References

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