  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.
