Exploring chaotic properties in the nonlinear Walecka Model

Abstract: This paper investigates dynamical properties of the Nonlinear Walecka Model (NLWM), also known as Quantum Hadrodynamics (QHD), which provides a relativistic framework for describing nuclear matter through nucleon-meson interactions. While the original linear model successfully captures qualitative features of nuclear matter, it overestimates nuclear compressibility; consequently, nonlinear extensions incorporating cubic and quartic self-interaction terms in the scalar field $(σ)$ are employed to achieve better agreement with experimental data. By treating the self consistent effective-mass equation as an iterative mapping, the study explores the emergence of complex behaviors such as periodic orbits and chaotic regimes. Using tools from nonlinear dynamics, including return maps and bifurcation diagrams, we characterize routes to chaos via period doubling cascades and identify the presence of "shrimps" stable isoperiodic islands within chaotic regions of the parameter space. Furthermore, we discusses the physical implications of these findings, suggesting that crisis phenomena and structural convergence may serve as dynamical signatures of macroscopic rearrangements in the scalar mean field, potentially influencing the stability and equation of state (EOS) of dense nuclear matter in extreme environments like neutron stars.