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We investigate the thermodynamic chaos of RN-AdS black holes immersed inPerfect Fluid Dark Matter by considering the dynamical equations of the fluidsystem evolved in the spinodal region. Based on the Melnikov method, it isshown that there exists a critical amplitude that affects the temporal chaos.And the influence of black holes charge and state parameter on the criticalamplitude is investigated with specific initial temperature. Then, forinevitable spatial chaos, three different types of portraits are discssuedaccording to the difference between the phase transition pressure and theambient pressure. Additionally, we check the local equilibrium near saddlepoints which shows that spatial chaos always exists regardless of theperturbation intensity.

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