Abstract

Mathematical modeling provides a powerful framework for insight into current scientific theories as well as hypothesis generation for further research. Despite its undeniable potential to enrich scientific advancement, the application of mathematical modeling remains conspicuously scarce in the field of family science. The complexity inherent in family dynamics, coupled with the intricate interplay of emotions in the individual, underscores the necessity of a robust analytical approach. Addressing this critical gap in the literature, this thesis introduces a sophisticated mathematical model of family dynamics integrating essential elements from family systems theory, emotion dynamics, and appraisal theory. The model is implemented as a versatile computer program capable of simulating family interaction over time, and allows for customization to suit specific research needs. Noteworthy outcomes from the current model parameters include the emergence of both asymptotic and periodic emotion dynamics, the significant influence of family roles on behavior and rapport, and the ripple effect of a single individual's behavior on the system as a whole. Through the exploration of emergent behaviors, this model offers invaluable insights and paves the way for future mathematical modeling and advancements in family science research.

Degree

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

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