Comparison of neural and traditional techniques for soliton structures and dynamical behavior in a double-chain DNA model

In this study, the nonlinear wave dynamics of the Double-Chain DNA model, a molecular system that captures the longitudinal and transverse interactions between two complementary nucleotide chains, are investigated. To construct explicit analytical structures, the generalized Riccati equation mapping method and the modified generalized Riccati mapping neural network method are applied in a complementary manner. Through these approaches, several classes of exact solutions, including hyperbolic, trigonometric, rational, and hybrid waveforms, are systematically derived. Consequently, the spectrum of admissible bright, dark, kink, and anti-kink wave structures supported by the model is significantly expanded. In addition to the derivation of exact solutions, the governing system is reduced to a planar dynamical framework to examine its qualitative behavior. Lyapunov exponent analysis is performed to quantify the long-term stability characteristics of the system and to identify parameter regimes exhibiting strong sensitivity to initial conditions. The analytical findings are further illustrated through 3D surface plots, contour diagrams, and 2D profiles, confirming the geometric and physical consistency of the obtained wave structures.