Bardeen thin-shell wormholes surrounded by fluid of strings

This study investigates the construction and stability of thin-shell wormholes formed by gluing two identical forms of Bardeen-AdS black holes, surrounded by a fluid of strings, within the framework of nonlinear electrodynamics. Using the cut-and-paste method and the Israel-Darmois formalism, we analytically derive the surface stress–energy components and formulate the corresponding effective potential governing the dynamics of the wormhole throat. To assess stability under linear radial perturbations, we analyze the second derivative of the potential and derive exact expressions for the equation of state parameters for three different matter models: barotropic, phantomlike variable, and Chaplygin variable equation of state. These expressions are inserted to obtain physically consistent and constraint-driven stability conditions. Our results show that the stability of the wormhole configurations is highly sensitive to the black hole parameters. We find that increasing the charge significantly enhances the stability regions, while moderate values of $\beta \approx 2$ yield optimal stability. Among the three equation of state models, the Chaplygin variable equation of state offers the most robust and extended stable configurations, particularly for small values of the radial dependence parameter $n$, outperforming the barotropic and phantomlike models in maintaining equilibrium with minimal exotic matter.