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198285 https://hdl.handle.net/2286/R.2.N.198285 http://rightsstatements.org/vocab/InC/1.0/ All Rights Reserved 2024 281 pages Doctoral Dissertation Academic theses Text eng Rodriguez, Lucero Kang, Yun Cooke, Nancy Li, Xianping Arizona State University Partial requirement for: Ph.D., Arizona State University, 2024 Field of study: Applied Mathematics for the Life and Social Sciences Interactions among individuals and entities shape the dynamics of systems across various domains, from ecological populations to human societies and human-automation interfaces. In this dissertation, I investigate cooperation behavior and its implications at different levels of goal complexity within diverse types of interactions. First, I delve into the exploration of human-automation interaction by investigating the dynamics of trust in autonomous systems. By examining key elements that influence human trust and decision-making in a changing environment, I illuminate how trust influences collaboration and performance in human-autonomy teams. Lastly, I propose a dynamic modeling framework to measure human trust in automation. Transitioning to human-human interaction, I investigate communication dynamics within teams and their impact on performance. Through a mathematical modeling framework, I explore how effective communication fosters cooperation among team members, enabling them to achieve shared goals in diverse task environments. This project underlines the importance of communication in navigating and completing complex team tasks. The subsequent Chapter 4 delves into human-nature interaction, exploring natural resource exploitation and its preservation for cancer treatment. Through mathematical modeling, I investigate strategies to sustainably manage natural resources while meeting public health needs. This highlights the complexity of balancing human interests with the preservation of the ecosystem. In the domain of inter-species interaction, Chapter 5 examines the cooperative behaviors within ant colonies, where ants collaborate to achieve collective goals such as successful nest growth and founding. By studying the dynamics of different nest founding strategies from queen ants, I investigate how cooperation facilitates complex tasks and influences colony survival, shedding light on the adaptive significance of social organization in insects. By combining findings across these projects, this dissertation offers insights into the fundamental aspects of cooperation and goal complexity in different interactive contexts. It contributes to my understanding of how cooperation impacts relationships and dynamics from an individual level to a group level in domains ranging from ecology to human teams. These findings inform strategies for advancing and strengthening collaboration in complex environments. Mathematics Ecology Psychology Communication Human-Autonomy Human-Nature Interactions Mathematical Modeling Social Dynamics Mathematical Modeling of Collective Interactions Among Agents