Chaos in the near-horizon dynamics of the dyonic $\rm{AdS_4}$-Reissner-Nordström black hole

Abstract: We investigate the chaos in the dynamics of a probe massless particle confined by the harmonic potential near the horizon of the dyonic $\rm{AdS_4}$-Reissner-Nordström black hole. The total energy of the particle, chemical potential and magnetic field in this system serving as independently adjustable parameters tune nonlinearity and phase-space structure. By analyzing the trajectories on the Poincaré section and evaluating the Lyapunov exponents, we obtain the dynamical phase diagrams of the chaos and find their counteracting regulatory role: at low energy, chaos is enhanced and the Lyapunov exponent $λ_L$ violates its upper bound (i.e. surface gravity) in the extremal black hole limit(combined paramete $Γ=3$); at high energy, the same extremal limit suppresses chaos, with $λ_L$ dropping to zero and a regular dynamical corridor emerging along $Γ=3$ in the dynamical phase diagrams. These results establish a direct mapping between black hole thermodynamics and microscopic chaos, offering new insights into the AdS/QCD correspondence and nonlinear dynamics in strongly curved spacetimes.