# Suppression of macroscopic oscillations in mixed populations of active and inactive oscillators coupled through lattice Laplacian

## TL;DR

This paper develops a theoretical framework to understand how mixed populations of active and inactive oscillators can have their synchronized oscillations suppressed through local diffusive coupling, with applications to epileptic seizure modeling.

## Contribution

It introduces an approximate stability criterion based on the system's free energy and highlights the role of effective wavenumber and spatial arrangement in suppression.

## Key findings

- Effective suppression depends on the spatial arrangement of oscillators.
- The theory is validated with a cortico-thalamic model of epilepsy.
- Suppression is influenced by population ratio and intensity.

## Abstract

We consider suppression of macroscopic synchronized oscillations in mixed populations of active and inactive oscillators with local diffusive coupling, described by a lattice complex Ginzburg-Landau model with discrete Laplacian in general dimensions. Approximate expression for the stability of the non-oscillatory stationary state is derived on the basis of the generalized free energy of the system. We show that an effective wavenumber of the system determined by the spatial arrangement of the active and inactive oscillators is an decisive factor in the suppression, in addition to the ratio of active population to inactive population and relative intensity of each population. The effectiveness of the proposed theory is illustrated with a cortico-thalamic model of epileptic seizures, where active and inactive oscillators correspond to epileptic foci and healthy cerebral cortex tissue, respectively.