Generative artificial intelligence (GenAI) is rapidly advancing, providing innovative tools and methods for a wide range of applications. Among these, Generative Agents, a key domain in GenAI, are valued for their fine-grained definitions and simulations of human-like behaviors. These agents provide new avenues for studying and modeling various domains, including social interactions, education, and cognitive sciences. However, existing works suffer from cognitive dynamics disconnect and affective absence, which hinder researchers from exploring human-related cognitive processes in depth. To address these limitations, we propose EvoAgents, a novel cognitive-driven framework that pioneers the exploration of dynamic personality evolution in Generative Agents. By defining the emotional content of agents and integrating a cyclical personality evolution cycle, EvoAgents represent a significant step toward creating more adaptive and authentic agent behaviors. Comprehensive simulations and evaluations show that EvoAgents achieve superior performance in key automated metrics compared to prior work, while uniquely enabling reasonable and robust personality evolution processes that align with cognitive and psychological expectations. By constructing a new simulation environment, SmallClassroom, based on the EvoAgents framework, we validate the framework's ability to provide deeper cognitive insights into social dynamics, aligning closely with established psychological theories.