Torus bifurcation and homoclinic chaos underlie potassium-driven epileptiform dynamics in a multi-timescale neural mass model

Epileptiform discharges originate from abnormal neuronal oscillations and constitute a core pathophysiological feature of epileptic seizures. Although frequently linked to potassium channel dysregulation, the specific dynamical mechanisms governing the generation and transition of these rhythms remain incompletely understood. To address this gap, we analyze a conductance-based neural mass model that bridges ion channel properties and population-level dynamics. By integrating geometric singular perturbation theory (GSPT), Shilnikov theory, and numerical bifurcation techniques, we elucidate how potassium channel parameters regulate oscillatory behavior. Our results demonstrate that reduced potassium conductance triggers a transition to quasiperiodic dynamics via a torus bifurcation, which is shown to arise through two distinct toroidal mechanisms. Following torus breakdown, the system undergoes a period-doubling cascade into spiral chaos, mediated by a Shilnikov-type saddle-focus homoclinic orbit, for which we provide a rigorous proof of existence. In contrast, variations in the potassium reversal potential primarily reshape the morphology of the chaotic attractor. Furthermore, we identify a novel canard-delayed-Hopf (CDH) singularity emerging from the model’s three-timescale structure, which organizes mixed-mode oscillations (MMOs) and governs the transition to epileptiform events. Extending the model to incorporate dopaminergic modulation reveals a concentration-dependent, biphasic regulation of both firing rates and bifurcation structure, offering a dynamical framework for integrating neuromodulation into computational models. Collectively, this work establishes a unified dynamical framework that links ion channel dysfunction to pathological brain rhythms and provides an extensible modeling foundation for developing neuromodulation-based therapies.