Cluster synchronization in Boolean neuronal networks: Roles of temperature, time-delay and network topology

Precise temporal coordination of neuronal firing is fundamental to information processing in the brain. However, how environmental factors such as temperature interact with intrinsic network properties, particularly signal transmission delays and connectivity topology, to shape collective neural dynamics remains poorly understood. Here, we use biophysically realistic, temperature-dependent Hodgkin–Huxley neuron model to uncover how temperature and time delay (transmission delay and process delay) jointly govern the emergence, diversity, and stability of cluster synchronization states. Our findings indicate that temperature, akin to time delay, is a key regulatory factor and exerts a pronounced impact on the parameter domains and transitions between different cluster states. Furthermore, our results reveal that the of cluster synchronization states are largely predicted by an extended greatest common divisor (GCD) theory. However, we also demonstrate that specific network architectures and temperature ranges can cause deviations from these predictions, resulting in novel synchronization patterns. These findings provide a generalizable framework for understanding how physical and environmental parameters regulate neural population dynamics. They also suggest new principles for designing robust brain-inspired networks and for developing interventions in temperature-sensitive neurological conditions.