A GEOMETRIC FRAMEWORK TO CHARACTERIZE STATE-DEPENDENT FORCED DYNAMICS IN SPIKING NETWORKS

Periodic forcing is often used to shape and control neural dynamics, but its effects vary across brain states. Depending on the network’s baseline dynamics, identical stimulation can entrain oscillations, suppress synchrony, or reorganize population activity. This makes responses difficult to compare across conditions, motivating a state-dependent characterization of stimulation effects.
To this end, we investigated how sinusoidal forcing reshapes population dynamics in a recurrent spiking network model across baseline regimes. We systematically tuned intrinsic parameters to generate different unforced dynamical states, then varied stimulation frequency and amplitude to investigate the forced bifurcation landscape and map where the network exhibits synchronization regions (Arnold tongues in the frequency-amplitude plane) and where transitions between dynamical states occur.
For each condition, we constructed a stroboscopic representation of the response and quantified the geometry of the resulting trajectories to obtain signatures of dynamical states and transitions across the parameter plane. Using this framework, we show that the emergent patterns can vary substantially with baseline dynamics, producing qualitative changes in tongue boundaries, widths, and topology.
Notably, projecting the dynamics onto a low-dimensional state space yields a geometric representation that makes responses more comparable across regimes and reduces sensitivity to baseline variability. This matters both for interpreting network dynamics under periodic forcing and for designing robust stimulation protocols whose effects can be predicted and optimized in a state-dependent manner, with potential relevance for disorders involving abnormal oscillations and synchrony.