Integrating generative artificial intelligence (AI) tools like ChatGPT into education has reshaped academic practices, offering students innovative ways to engage with learning tasks. This study examines the cognitive, emotional, and behavioral factors influencing undergraduate students' engagement with ChatGPT, guided by the technology acceptance model, the stimulus-organism-response framework, and attachment theory. Using a sample of 398 US undergraduates, the study employed confirmatory factor analysis and structural equation modeling to validate relationships among perceived usability, enjoyment, responsiveness, learning motivation, emotional attachment, satisfaction, and continuance intention. Results revealed that perceived responsiveness is a significant driver of learning motivation, emotional attachment, and satisfaction, while perceived enjoyment enhances learning motivation and satisfaction. Emotional attachment strongly predicts continuance intention, emphasizing the role of affective connections in sustained use. The findings indicate that successful AI tools must balance usability, responsiveness, and emotional engagement to foster long-term adoption. This research advances the theoretical understanding of human-AI interactions in education and provides practical recommendations for designing effective, student-centered AI tools.