Temporal and Spatial Chaos of RN-AdS Black Holes Immersed in Perfect Fluid Dark Matter

We investigate the thermodynamic chaos of RN-AdS black holes immersed in Perfect Fluid Dark Matter by considering the dynamical equations of the fluid system evolved in the spinodal region. Based on the Melnikov method, it is shown that there exists a critical amplitude that affects the temporal chaos. And the influence of black holes charge and state parameter on the critical amplitude is investigated with specific initial temperature. Then, for inevitable spatial chaos, three different types of portraits are discssued according to the difference between the phase transition pressure and the ambient pressure. Additionally, we check the local equilibrium near saddle points which shows that spatial chaos always exists regardless of the perturbation intensity.