Frequency-dependent synchronization in blinking networks: insights from Hindmarsh–Rose, Lorenz, and Rössler systems

Abstract

This study examines how the temporal structure of network couplings affects synchronization, a fundamental phenomenon in numerous real-world systems. Focusing on blinking networks, a class of time-varying networks where couplings periodically switch on and off, we compare two distinct blinking schemes across three canonical dynamical systems: the Hindmarsh–Rose, Lorenz, and Rössler systems. Using the Master Stability Function (MSF) framework, we reveal a striking contrast in synchronization behavior. When all couplings are activated simultaneously during the same portion of the blinking period, the system’s synchronization stability remains unaffected by the blinking frequency, closely resembling that of an averaged static network characterized by a linear MSF profile. In contrast, when couplings are activated sequentially within each blinking period, this linear MSF pattern emerges only at high blinking frequencies (fast blinking). At lower frequencies (slow blinking), the MSF exhibits diverse, system-specific patterns. Notably, the linear MSF pattern ensures the emergence of synchronization irrespective of the underlying structural properties. Thus, these findings offer new insights into how the temporal organization of couplings governs collective dynamics in time-varying networks, particularly in contexts where the emergence and stability of synchronization are critical.