Propagation of small-amplitude quantum ion-acoustic waves and its fractal representations is investigated in an electron-ion quantum plasma with separated spin electrons in the framework of the KdV and EKdV equations derived using reductive perturbation technique. These two equations are transformed into planar dynamical systems by using suitable traveling wave transformation. Qualitatively different phase portraits of these two systems are drawn with their respective Sagdeev’s pseudopotential curves and surface plots. Distinct orbits in the phase portraits give rise to distinct wave solutions. Periodic and superperiodic wave solutions are investigated numerically and solitary wave solutions are derived analytically. The effect of parameters such as Mach number, direction cosine, spin polarization and frequency ratio on these wave solutions are presented. For instance, it is seen that the spin density polarization ratio has an impressive effect on the amplitude of the wave solution, while the frequency ratio has no effect on its amplitude. Also, we have provided a physical explanation for our finding. Further, the dynamical features of the original system and reconstructed system using fractal interpolation function are investigated under the external forcing term. Chaotic and quasiperiodic phenomena are observed for different initial conditions. The results may help to better understand the degenerate electron gas that exists in dense astrophysical bodies.
