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Dynamical observations and range of diverse soliton profiles for a nonlinear double-chain deoxyribonucleic acid model

Author

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  • Ejaz, Ayesha
  • Amjad, Zeeshan
  • Raza, Nauman
  • Wong, Patricia J.Y.
  • Almalki, Yahya

Abstract

This study explores the nonlinear (2+1)-dimensional double-chain deoxyribonucleic acid (DNA) model, which plays a central role in fundamental biological processes such as replication, transcription, and translation. Utilizing the G′/(bG′+G+a)-expansion method, we derive new exact solutions in the domain of hyperbolic and trigonometric functions. Various soliton structures, such as kink, singular, and singular periodic solitons, are constructed and illustrated through 3D, density, and 2D profiles by means of suitable parameter choices. A qualitative analysis is carried out using the concepts of bifurcation and chaos theory to gain deeper insights. A parameter-dependent bifurcation analysis reveals how minute alterations in parameters can instigate significant fluctuations in system stability. More specifically, a perturbation term is introduced to investigate chaotic responses, which are verified by different detecting tools, Kaplan–Yorke dimension and multistability. To further emphasize the dynamic nature of the model, sensitivity analysis is performed under three distinct initial conditions. These findings expand our understanding of the nonlinear nature of DNA systems and provide fresh perspectives on their stability and complexity.

Suggested Citation

  • Ejaz, Ayesha & Amjad, Zeeshan & Raza, Nauman & Wong, Patricia J.Y. & Almalki, Yahya, 2026. "Dynamical observations and range of diverse soliton profiles for a nonlinear double-chain deoxyribonucleic acid model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 527-541.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pb:p:527-541
    DOI: 10.1016/j.matcom.2025.10.028
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