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This paper investigates the dynamics of the timelike and null geodesics near the Bardeen-AdS black hole immersed in quintessence. Specifically, the equation of geodesic motion is derived by solving the Hamilton–Jacobi equation of the test particles, including the timelike particles, neutrinos, and photons. Due to the nonlinear electrodynamics' effect on this black hole spacetime, photon motion is governed by the effective geometry, not the spacetime geometry. Furthermore, the study examines attracting, escaping, and bound orbits, and illustrates some orbits with intriguing shapes. The test particles' circular orbits (general circular orbits and innermost/outermost stable circular orbits) are discussed in detail, wherein these orbits are principally affected by the impact parameter, the magnetic charge, and the quintessential normalization constant. In particular, the presence of quintessence makes the spacetime structure of the black hole more complex. This results in a greater number of circular orbits for the particles around it and a more diverse shape for the curve of the radius of the circular orbit with the magnetic charge. The stability of the timelike geodesics is analyzed by calculating the Lyapunov exponent. In addition, the properties of black hole horizons are presented. Finally, the critical magnetic charge and critical quintessential normalization constant, with which two horizons merge into one, are discussed.
Wang et al. (Mon,) studied this question.