This paper explores the impact of reputation-based imitation-mutation dynamics on the evolution of cooperation in evolutionary games. The authors introduce a new model that combines imitation and random strategy mutations, allowing for the exploration of irrational decision-making and psychological factors in collective behavior. The study focuses on two social dilemma games: the Prisoner's Dilemma (PDG) and the Snowdrift Game (SDG), and examines the effects of different interaction topologies, including lattices, small-world, and scale-free networks. The key findings include: 1. **Imitation-Mutation Dynamics**: The extended dynamics, which include both imitation and random mutations, significantly enhance cooperation levels compared to traditional imitation dynamics, especially in high-temptation regions of the PDG. 2. **Reputation Mechanism**: Reputation, which is directly linked to accumulated payoffs, plays a crucial role in influencing strategy updates. The reputation mechanism helps individuals resist defection, particularly in high-temptation situations. 3. **Network Topology**: Different interaction topologies affect the evolution of cooperation, with lattices and random graphs showing more stable cooperation levels than scale-free networks. 4. **Parameter Analysis**: The parameters $\alpha$ (reputation update coefficient) and $m$ (mutation rate) significantly influence cooperation levels. Larger $\alpha$ values can increase cooperation in low-temptation regions but can lead to decreased cooperation in high-temptation regions. Higher $m$ values reduce the effectiveness of the reputation mechanism, stabilizing cooperation at lower levels. 5. **Conclusion**: The combination of imitation and mutation dynamics, along with a generalized fitness function, provides a more realistic model for understanding the evolution of cooperation in complex social systems. The study highlights the importance of considering both rational and irrational decision-making processes in evolutionary game theory. The research contributes to the field by providing a more nuanced understanding of how reputation and mutation mechanisms can influence the emergence and maintenance of cooperation in various social contexts.This paper explores the impact of reputation-based imitation-mutation dynamics on the evolution of cooperation in evolutionary games. The authors introduce a new model that combines imitation and random strategy mutations, allowing for the exploration of irrational decision-making and psychological factors in collective behavior. The study focuses on two social dilemma games: the Prisoner's Dilemma (PDG) and the Snowdrift Game (SDG), and examines the effects of different interaction topologies, including lattices, small-world, and scale-free networks. The key findings include: 1. **Imitation-Mutation Dynamics**: The extended dynamics, which include both imitation and random mutations, significantly enhance cooperation levels compared to traditional imitation dynamics, especially in high-temptation regions of the PDG. 2. **Reputation Mechanism**: Reputation, which is directly linked to accumulated payoffs, plays a crucial role in influencing strategy updates. The reputation mechanism helps individuals resist defection, particularly in high-temptation situations. 3. **Network Topology**: Different interaction topologies affect the evolution of cooperation, with lattices and random graphs showing more stable cooperation levels than scale-free networks. 4. **Parameter Analysis**: The parameters $\alpha$ (reputation update coefficient) and $m$ (mutation rate) significantly influence cooperation levels. Larger $\alpha$ values can increase cooperation in low-temptation regions but can lead to decreased cooperation in high-temptation regions. Higher $m$ values reduce the effectiveness of the reputation mechanism, stabilizing cooperation at lower levels. 5. **Conclusion**: The combination of imitation and mutation dynamics, along with a generalized fitness function, provides a more realistic model for understanding the evolution of cooperation in complex social systems. The study highlights the importance of considering both rational and irrational decision-making processes in evolutionary game theory. The research contributes to the field by providing a more nuanced understanding of how reputation and mutation mechanisms can influence the emergence and maintenance of cooperation in various social contexts.