Phase- and amplitude-dependent control of synchronization in excitatory-inhibitory networks via pulsed stimulation

Abstract

Oscillatory neuronal networks exhibit complex collective responses to external perturbations that depend on both the intrinsic network dynamics and the timing of stimulation. Although phase response curves (PRCs) have become a standard tool for characterizing these responses, phase resetting alone provides an incomplete description of how transient perturbations reshape collective activity. Here, we investigate the dynamics of a balanced excitatory-inhibitory network of exponential integrate-and-fire (EIF) neurons subjected to phase-targeted current pulses. By jointly analyzing the network phase response curve (nPRC), network amplitude response curve (nARC), and changes in the population synchrony, we establish a framework for characterizing collective network responses in terms of phase, amplitude, and synchronization. We show that identical stimulation pulses can either enhance, suppress, or leave network synchronization unchanged depending solely on their phase within the oscillation cycle, revealing distinct synchronizing and desynchronizing windows. The nARC further identifies robust phase intervals that maximize suppression of oscillatory activity and provide optimal targets for repeated stimulation. Successive perturbations progressively desynchronize the network activity while continuously reshaping the phase, amplitude, and synchrony response landscapes, driving the network toward a modified dynamical state without altering the optimal stimulation phase. These cumulative effects remain robust across stimulation intensities, inhibitory synaptic time constants, and independent network realizations. Our results demonstrate that phase, amplitude, and synchronization represent complementary dynamical dimensions of oscillatory neuronal networks and provide general principles for the state-dependent control of collective dynamics through phase-targeted perturbations.