Analysis of Basins of Attraction in the Pseudo-Newtonian Photogravitational Restricted Four-Body Problem with Asteroid Belt Effects

In this study, we examine the convergence behavior of the Newton–Raphson basins of convergence in relation to the equilibrium points serving as attractors within the framework of the pseudo-Newtonian planar circular restricted four-body problem. This model accounts for the effects of both radiation pressure and the presence of a circular asteroid belt. Our focus lies on determining the positions and assessing the stability of these equilibrium points as the transition parameter, denoted by $$\epsilon $$ , is varied across the range [0, 1]. By employing a multivariate form of the Newton–Raphson iterative algorithm, we draw the basins of convergence across selected two-dimensional planes. A thorough numerical analysis is carried out to illustrate how changes in the transition parameter influence the structure and geometry of these convergence regions. Furthermore, we examine the relationship between the spatial extent of the attraction basins and the number of iterations needed to reach convergence. The results suggest that the behavior of these regions is complex yet deeply engaging, offering rich insights into the dynamics of the system.