This study presents a hybrid approach for analyzing animal behavior in T-maze tasks, combining traditional analytical modeling with advanced machine learning techniques. T-maze experiments are a well-established paradigm used to investigate decision-making processes in animals, where they must select one of two paths based on reinforcement feedback. To better understand the underlying cognitive mechanisms behind this, the proposed approach integrates conventional methods, such as decision theory and cognitive modeling, with cutting-edge machine learning algorithms, including deep learning models. This combination enables a more comprehensive analysis of the complexity inherent in animal behavior during decision-making tasks. Furthermore, we model the problem mathematically and apply fixed-point results to establish the existence and uniqueness of solutions to the proposed problem. This hybrid methodology not only improves the accuracy of behavioral predictions but also offers deeper insights into the decision-making process. The results show that integrating analytical methods with machine learning techniques leads to more robust and complex analyses compared to traditional approaches. This framework has significant implications for computational ethology, as it advances our understanding of animal cognition. Additionally, the study sets the foundation for future research in behavioral neuroscience, providing a valuable tool for modeling complex animal behaviors in various experimental settings. By bridging the gap between theory and data-driven approaches, this work paves the way for further interdisciplinary studies in the field of cognitive science.