the term "psyber mathematics" was not a well-established or widely recognized field in academia or research. It is possible that new developments have occurred since then, but I cannot provide specific examples of successful applications in this area. However, I can address the general use of mathematical models in the study of social cognition and interpersonal processes in neuroscience and psychology, which may be relevant to the broader concept of "psyber mathematics."
Social Network Analysis: Social network analysis uses graph theory and mathematical models to study the structure and dynamics of social networks. Researchers have applied this approach to understand how information, influence, and relationships spread within social groups and how individual behaviors are influenced by their network connections.
Game Theory and Cooperation: Game theory is a mathematical framework used to analyze strategic decision-making in competitive and cooperative situations. Researchers have employed game theory to study cooperation, trust, and reciprocity in social interactions.
Dynamic Systems Modeling: Dynamic systems modeling involves using mathematical equations to describe and predict changes in complex systems over time. This approach has been applied to study the dynamics of interpersonal relationships and how they evolve over the long term.
Neural Network Modeling: Neural network models, inspired by the brain's neural connections, have been used to simulate social cognitive processes. These models help understand how the brain processes social information, such as facial expressions, emotions, and social judgments.
Computational Models of Decision Making: Computational models are used to understand decision-making processes in social contexts. These models can account for factors like social norms, emotions, and prior experiences to predict how individuals make choices in social situations.
Statistical Models for Social Behavior Analysis: Statistical methods, such as regression analysis, structural equation modeling, and multilevel modeling, are commonly used in social cognitive research to identify relationships between variables and test hypotheses about social behavior and cognition.
Mathematical Models of Learning and Social Influence: Researchers use mathematical models to investigate how individuals learn from each other and how information spreads within a social group.
It is important to note that interdisciplinary research combining mathematics, neuroscience, and psychology is continually evolving. Advances in computational neuroscience, machine learning, and artificial intelligence may lead to more sophisticated mathematical models and novel applications in the study of social cognition and interpersonal processes. To get up-to-date information on specific developments in the field of "psyber mathematics," I recommend conducting a literature search using recent academic publications and reputable research databases.