Dynamical analysis of fractional-order DNA double chain model using chaotic approach and data points

Abstract This study examines the double chain deoxyribonucleic acid (DNA) model, which is essential for the transmission of genetic information. Polynucleotide chains are represented by two rods connected by an elastic membrane to model hydrogen bonds. The longitudinal and transverse displacements are calculated using the enhanced modified extended tanh expansion method, incorporating the fractional differential order of the model with the M-Truncated derivative. The results obtained are illustrated through 2D and 3D graphs, revealing precise wave patterns. The overlapping function can also be utilized to compare and visualize the solutions. After perturbations are introduced, the behavior of the system is examined using chaos detection methods, including power spectrum analysis, return maps, and basin attractor techniques. Nonlinear dynamics demonstrate sensitivity to initial conditions and time-decay dependence. This refers to the chaotic behavior of the DNA system under perturbation, in which small changes in the initial state can result in significantly diverse results over time. Through its description of the perturbation system, this multidisciplinary effort reveals hidden DNA properties, overcoming the gap between applied mathematics and experimental biology.