Regime Mapping of Oscillatory States in Balanced Spiking Networks with Multiple Time Scales

Balanced spiking networks can transition between silent, asynchronous-irregular, and oscillatory states depending on interacting synaptic and temporal time scales, while their joint parameter structure remains incompletely characterized. In this work, we systematically map how postsynaptic decay ({\tau}s), conduction delay (d), and plasticity rate ({\lambda}p) jointly shape oscillatory regimes in recurrent leaky integrate-and-fire networks. By combining Brian2 simulations across the ({\tau}s, d, {\lambda}p) space with a coarse Hopf-reference boundary, we construct regime maps that directly visualize SIL-AI-OSC transitions and corresponding spectral prominence landscapes. The mapped results show that increasing {\lambda}p expands oscillatory regions toward shorter {\tau}s and moderate-to-long delays, while prominence maps identify parameter regions with the strongest rhythmic coherence. Representative control experiments further connect this global landscape to local rhythm-forming mechanisms, showing that STDP freezing weakens rhythmic coherence whereas delay jitter enhances it with minimal change in mean firing rate. As a result, these findings provide a useful reference for operating-point selection, synchrony modulation studies, and future biologically grounded spiking-network modeling within similar balanced-network settings.