In this paper, we develop a complexity factor for static sphere in modified Gauss–Bonnet gravity with anisotropic and nonhomogeneous configuration. We use the field equations as well as equation of continuity to derive expressions for mass function in [Formula: see text] gravity. The Riemann tensor is split using Bel’s approach to formulate structure scalars that exhibit fundamental properties of the system. A complexity factor is developed on the basis of these scalars and the condition of vanishing complexity is used to obtain solutions of two different models. It is observed that modified terms increase complexity of the matter distribution.

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The concept of complexity for dynamical spherically symmetric dissipative self-gravitating configuration [1] is generalized in the scenario of modified Gauss-Bonnet gravity. For this purpose, a spherically symmetric fluid with locally anisotropic, dissipative, and non-dissipative configuration is considered. We choose the same complexity factor for the structure as we did for the static case, while we consider the homologous condition for the simplest pattern of evolution. In this approach, we formulate structure scalars that demonstrate the essential properties of the system. A fluid distribution that fulfills the vanishing complexity constraint and proceeds homologously corresponds to isotropic, geodesic, homogeneous, and shear-free fluid. In the dissipative case, the fluid is still geodesic but it is shearing, and there is a wide range of solutions. In the last, the stability of vanishing complexity is examined.

Through this study, we intend to present a comprehensive summary of the most recent research on complex systems or complexity factor [Formula: see text] in the background of modified gravity theories (MGT). In this way, we examined [Formula: see text] for the novel MGT named [Formula: see text] gravity under the anisotropic static fluid configuration. [Formula: see text] is defined as one of the structure scalars [Formula: see text] which is trace-free component obtained from the orthogonal splitting of the Riemann tensor. Two mass approaches are used which have immense influence on [Formula: see text]. Furthermore, vanishing complexity condition is used with an eye towards finding the solution of the nonlinear system. Two extra models are explored which ensure one more condition for the purpose of comprehensive results.

The previous ideology of complexity factor for the dynamical spheres \cite{herrera2018definition,yousaf2022role} is extended for the influence of charge. A non-dissipative and dissipative dynamical spherically symmetric self-gravitating structure is examined in the presence of Maxwell $f(\mathcal{G})$ gravity to examine the complexity factor. The pattern of evolution is studied with the minimal complexity constraint. The complexity factor remains the same for the structure of fluid distribution, while we examine homologous constraints for the most basic evolution pattern. We calculate the structure scalars which play an important role in order to understand the fundamental properties of the system. The fluid is geodesic as well as shearing for the dissipative case and there is a large number of solutions. In the non-dissipative fluid distribution, a shear-free, homogeneous, and isotropic, geodesic fluid correlates with the evolving homologous and vanishing complexity condition. The implication of the condition of vanishing complexity factor and stability are discussed at the end.