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Abstract

Synchronization plays a central role in complex dynamical networks, underpinning phenomena across physics, neuroscience, and natural systems. Time-varying networks with blinking coupling mechanisms, where coupling switches cyclically among variables, offer a basic yet effective setting for studying synchronization. Our earlier work showed that adaptive, state-dependent blinking schemes can significantly enhance synchrony, but at the expense of high computational cost, particularly in large networks. In this study, we systematically examine how network connectivity patterns and system size affect synchronization cost. We analyze configurations ranging from two coupled systems to large-scale networks with complete, regular, small-world, scale-free, and random structures, and evaluate their performance across different network sizes and dynamical node systems. The results reveal that synchronization costs exhibit minimal variation with network structure or size, indicating that the underlying properties are robust and generalizable. These findings provide new insight into the efficiency and limitations of adaptive blinking coupling schemes, clarifying when their use is beneficial for promoting and sustaining network synchronization.