Dynamic Evolutionary Game and Convergence Analysis of Mining Pool Strategies Under DDoS Attacks for IoT-Oriented Blockchain Systems

Distributed Denial-of-Service (DDoS) attacks are a major security threat to blockchain systems, especially in Internet-of-Things (IoT)-oriented and edge-assisted deployments where mining services, gateway nodes, and communication resources are more vulnerable to disruption. In Proof-of-Work (PoW) blockchain networks, such attacks can degrade mining pool connectivity, reduce effective revenue, and undermine both system security and resilient infrastructure design. Existing studies have mainly focused on DDoS detection or static mining games, while paying limited attention to dynamic strategy evolution and convergence under varying network conditions. To address this problem, this paper proposes a dynamic evolutionary game (DEG)-based revenue model for mining pools under DDoS attacks. Unlike static game methods that only identify equilibrium points, this work analyzes both the convergence dynamics and the sensitivity of equilibrium outcomes to key parameters, including attack scale, penalty, reward, and network quality. The proposed method characterizes the adaptive interaction between honest mining and attack behaviors through replicator dynamics, and analyzes strategy stability and convergence using equilibrium and Lyapunov-based methods. In addition, we investigate how key system parameters, including attack scale, reward, penalty, and network quality, affect the convergence speed of mining pool strategies in different environments. MATLAB results show that the proposed DEG model better captures the dynamic evolution of mining pool behaviors than conventional static-game formulations. The results further indicate that improved network conditions may unintentionally incentivize DDoS attacks, while proper parameter tuning can accelerate convergence toward security-favorable strategies. These findings provide useful insights for secure blockchain design and resilient mining infrastructure in IoT-oriented systems.