Unveiling the intricacies of attracting zones in magnetic binary systems: Investigating the impact of Yukawa correction

This study delves into the restricted three-body problem with a Yukawa correction to Newtonian gravitational forces, focusing on magnetic binary systems. We scrutinize the influence of Yukawa correction parameters ($\alpha$, $\beta$) and the ratio of magnitude of magnetic moments ($\lambda$) on the system’s equilibrium points and their stability, zero-velocity curves. In our case, there exist of five and seven equilibrium points and all are found to be unstable for given range of parameters. Our examination extends to the basins of convergence and the existence of fractal under the influence of $\alpha$ and $\lambda$. Graphs drawn with the help of Wolfram Mathematica software vividly portray the parameter-driven evolution of equilibrium points, zero-velocity curves and basins of convergence. Furthermore, we explore the fractal characteristics within the basins of convergence, offering valuable insights into the complex dynamics of magnetic binary systems with Yukawa correction.