Chaos in the near-horizon dynamics of the dyonic $\rm{AdS_4}$-Reissner-Nordstr\"{o}m 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-Nordstr\"om 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 Poincar\'e 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 $\lambda_L$ violates its upper bound (i.e. surface gravity) in the extremal black hole limit(combined paramete $\Gamma=3$); at high energy, the same extremal limit suppresses chaos, with $\lambda_L$ dropping to zero and a regular dynamical corridor emerging along $\Gamma=3$ 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.