  In this paper, we consider the effect of electromagnetic field to the
definition of complexity in the context of $f(G,T)$ gravity, where $G$ and $T$
express the Gauss-Bonnet term and energy-momentum tensor, respectively. The
physical parameters such as anisotropic pressure, charge, energy density
inhomogeneity, heat dissipation and correction terms are found responsible to
induce complexity within the self-gravitating objects. The scalar functions are
determined using Herrera's orthogonal splitting approach, which results in a
complexity factor that includes all of the system's essential features.
Furthermore, we investigate the dynamics of charged spherical distribution by
choosing homologous mode as the simplest evolutionary pattern. Dissipative and
non-dissipative cases associated with complexity free and homologous conditions
are also discussed. Finally, we study the components responsible for producing
complexity during the evolution process. We deduce that the inclusion of extra
curvature terms and charge in $f(G, T)$ gravity enhances the complexity of the
self-gravitating structure.
