Abstract
Epileptic seizures are increasingly studied as network-level dynamical events, but it remains difficult to relate local bursting mechanisms to topology-dependent synchronization and spread. We study this issue in a reduced graph model of diffusively coupled Hindmarsh-Rose (HR) bursting units. Each node is interpreted as a mesoscopic excitable element rather than a literal single neuron, and seizure-like activity is defined operationally as sustained high-amplitude bursting. For this class of models we derive a master-stability formulation that separates local HR dynamics from graph topology and yields spectral criteria for the local transverse stability of synchronous bursting in terms of Laplacian eigenvalues and coupling strength. Numerical simulations on idealized chain, ring, small-world, and scale-free networks are used to compare these predicted synchronization thresholds with direct network dynamics and to illustrate regimes of asynchronous bursting, partial synchronization, and rapid recruitment. We also examine how autaptic feedback, post-inhibitory rebound, and inhibitory currents modify the local variational dynamics and thereby shift the network-level synchronization window. The framework is intended as an analytically transparent complement to more detailed neural-mass and epileptor models: it clarifies how graph spectra can organize seizure-like synchronization in a simplified HR setting, while its clinical interpretation remains qualitative and subject to further validation.