Chaotic motion of particles around a dyonic Kerr–Newman black hole immersed in the Melvin-swirling universe

Abstract We employ the Poincaré section, fast Lyapunov indicator, recurrence analysis, bifurcation diagram and basins of attraction to investigate the dynamical behaviors of the motion of particles around a new dyonic Kerr–Newman black hole immersed in the Melvin-swirling universe presented in (Di Pinto et al. in J High Energy Phys 06:150, 2025). We note that the swirling parameter j and magnetic field strength B make the equations of motion for particles nonseparable, and confirm the presence of chaotic behavior in the motion in this dyonic Kerr–Newman–Melvin-swirling spacetime and its sub-cases by removing the conical singularities and removing both the conical singularities and the Dirac strings. We observe that both the number of chaotic orbits and the chaotic region increase with the increase of the parameters j and B , but decrease as the electric charge Q , magnetic charge H or spin parameter a increases. Moreover, we find that the presence of j changes the ranges of B , Q , H and a where the chaotic motion appears for particles. The swirling parameter together with the magnetic field strength, electric charge, magnetic charge and spin parameter yields richer physics in the motion of particles for the spacetime of a dyonic Kerr–Newman black hole immersed in the Melvin-swirling universe.