Topology-Dependent Stability Performance of Energy Flow Networks

This paper studies the stability of energy flow dynamics in complex networks, emphasizing the impact of representative topological structures on control performance. Such networks frequently appear in transportation, power distribution, financial, and demographic systems, where nodes and edges represent hosts and transmitters of energy. Motivated by the critical role of topology in physical and engineering contexts, we focus on canonical network prototypes, including small-world and related structures observed in practice. A unified dynamic model is presented, and stability is quantified using L₁/L_∞ and Hankel norms. Extensive numerical experiments on statistically robust, large-scale networks illustrate how subtle topological variations significantly influence stability behaviors. These results offer theoretical insights and practical guidance for enhancing the control of energy flow in complex networks.