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Exploring quasi-periodic behavior, bifurcation, and traveling wave solutions in the double-chain DNA model

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  • Beenish,
  • Samreen, Maria

Abstract

The double-chain DNA model, which is essential for genetic material transmission and retention, is examined in this work. The model shows two long, evenly elastic filaments joined by hydrogen bonds between base pairs, which represent DNA’s polynucleotide chains. To reduce complexity and derive solutions for differential equations with symmetries, the Lie symmetry technique is a powerful mathematical tool. The sardar sub-equation and logistic equation techniques are used to produce traveling wave solutions, and graphical representations are used to show relationships and structures in the data. A Galilean transformation serves to change the model from a second-order ODE into a system of first-order differential equations. For qualitative evaluations, bifurcation analysis is used. Afterward, an external force is injected, changing the system and generating chaotic behavior to be revealed by chaos detection techniques. These results provide important new understandings of mathematical physics and soliton dynamics.

Suggested Citation

  • Beenish, & Samreen, Maria, 2025. "Exploring quasi-periodic behavior, bifurcation, and traveling wave solutions in the double-chain DNA model," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000657
    DOI: 10.1016/j.chaos.2025.116052
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    References listed on IDEAS

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    1. Seadawy, Aly R. & Bilal, M. & Younis, M. & Rizvi, S.T.R. & Althobaiti, Saad & Makhlouf, M.M., 2021. "Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Jhangeer, Adil & Beenish,, 2024. "Ferroelectric frontiers: Navigating phase portraits, chaos, multistability and sensitivity in thin-film dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    3. Wael W. Mohammed & A. M. Albalahi & S. Albadrani & E. S. Aly & R Sidaoui & A. E. Matouk & A. M. Nagy, 2022. "The Analytical Solutions of the Stochastic Fractional Kuramoto–Sivashinsky Equation by Using the Riccati Equation Method," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-8, May.
    4. Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R. & Ali, Kashif, 2022. "Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
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