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

Abstract

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 (τs), conduction delay (d), and plasticity rate (λp) jointly shape oscillatory regimes in recurrent leaky integrate-and-fire networks. By combining Brian2 simulations across the (τs, d, λp) 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 λp expands oscillatory regions toward shorter τs 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.

Figures (2)

• Figure 1: Regime maps of a balanced spiking network under PSP decay ($\tau_s$), delay ($d$), and plasticity rate ($\lambda_p$). For each $\lambda_p$ slice, the top row shows the mean regime classification across five seeds (SIL, AI, and OSC), with the white dashed line indicating a coarse Hopf-reference boundary for the AI--OSC transition. The bottom row shows the corresponding mean PSD prominence. The mapped parameter space spans $\tau_s=5$--30 ms and $d=0$--10 ms, providing an exploratory map of SIL--AI--OSC transitions.
• Figure 2: Control experiments in a representative oscillatory regime. The operating point was selected from the highest-prominence region of the $\lambda_p=2\times10^{-3}$ slice ($\tau_s=5$ ms, $d=6.25$ ms). The top row shows spike rasters under Baseline, Freeze, and Jitter conditions, the middle row shows population firing-rate traces, and the bottom row shows power spectra (5--100 Hz) with the dominant frequency ($f_0$) and spectral prominence (Prom).