Fractal basins of attraction in a binary quasar model.

• The position of equilibrium points are monitored with respect to the parameters the distances between galaxies (R), the masses of disk and nucleus of galaxies (M d 1 , M n 1 , M d 2 , M n 2 ). • The zero velocity curves are investigated under the effect of above parameters. • We determine the Newton-Raphson's basins of attraction associated with the libration points. • The existence of unpredictable (fractal) regions are explored using the method of basin entropy. • Due to variation of the parameter R, the change in basin entropy (S b) and boundary basin entropy (S bb) is graphically shown. The present paper investigates the binary system of quasars in the framework of the Circular Restricted Three-Body Problem. The parametric evolution of libration points and the geometry of zero-velocity curves are one of the crucial aspects of our study. The multivariate form of NR method is applied to study the basin of attraction connected with libration points. The algorithm for using the Newton-Raphson method is slightly modified in order to avoid the unnecessary delay in the convergence of initial conditions. The impact of parameters on the pattern of the basin of attraction and the number of iterations needed for the convergence of initial conditions are explored. We carry out an exhaustive (numerical) study to show the influence of these parameters on converging regions in basins of attraction. We unveil the existence of fractal structure in the basin of attraction using the method of basin entropy. In almost all cases, the existence of fractal structure is found throughout the basins of attraction. [ABSTRACT FROM AUTHOR]