Analyzing the double-chain deoxyribonucleic acid model: bifurcation, chaos, and sensitivity insights through advanced analytical techniques.

Abstract

This study advances the understanding of genetic transmission by exploring the dynamic behavior of double-chain deoxyribonucleic acid (DNA) through a newly established dynamic model using the Galilean transformation. Using planar dynamical systems theory, we apply bifurcation techniques to reveal the model's sensitivity to initial conditions and assess its stability, supported by numerical simulations via the Runge-Kutta method. To explore chaotic dynamics, we introduce perturbations and perform a detailed analysis using two-phase portraiture, two-dimensional phase diagrams, and Lyapunov exponents. Furthermore, we derive novel soliton solutions using the improved generalized Riccati method and the double expansion technique. Graphical results generated in MATLAB illustrate key features such as bifurcation points, conditions for chaos, and the influence of perturbations, providing deeper insights into DNA dynamics. Overall, this research enhances theoretical understanding while bridging applied mathematics and experimental biology, offering valuable perspectives on the complex behavior of DNA.