Shock waves and adiabatic trapping in relativistic quantum degenerate plasmas: Exploring periodic, quasiperiodic and chaotic behavior

Ion acoustic shock waves are investigated in relativistic quantum degenerate plasmas, which are characterized by their ultra-high densities. Our investigation employs a nonlinear equation that has a 3/2 order fractional power. We investigate the intricate interplay between the adiabatically trapped electrons and the shock front by employing phase portrait analysis of a planar dynamical system that has not been considered earlier. This exploration allows us to understand the effects of various controlling parameters on the shock profile, steepness, and associated dynamics. An external periodic force is introduced in the current mathematical model to investigate the quasiperiodic and chaotic behavior of the system. Additionally, Poincaré sections, Fast Fourier Transformations, bifurcation analysis, and sensitivity analysis are performed to reveal the quasiperiodic and chaotic nature of the attractor of the nonlinear dynamical system. It is observed that the commensurable and incommensurable characteristics of the natural frequency and external periodic force frequency of the system play a significant role in the system's quasiperiodic and chaotic behavior. The findings not only deepen our understanding of shock waves in relativistic quantum degenerate plasmas but also have broader implications for various applications in astrophysics and nonlinear dynamics. This work also highlights the quasiperiodic and chaotic behavior of the system as the external periodic force varies by considering the commensurability of the system's frequencies.