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Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model

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  • Ali, Khalid K.
  • Cattani, Carlo
  • Gómez-Aguilar, J.F.
  • Baleanu, Dumitru
  • Osman, M.S.

Abstract

In this work, we introduce a numerical and analytical study of the Peyrard-Bishop DNA dynamic model equation. This model is studied analytically by hyperbolic and exponential ansatz methods and numerically by finite difference method. A comparison between the results obtained by the analytical methods and the numerical method is investigated. Furthermore, some figures are introduced to show how accurate the solutions will be obtained from the analytical and numerical methods.

Suggested Citation

  • Ali, Khalid K. & Cattani, Carlo & Gómez-Aguilar, J.F. & Baleanu, Dumitru & Osman, M.S., 2020. "Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304860
    DOI: 10.1016/j.chaos.2020.110089
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    References listed on IDEAS

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    1. Lu, D. & Osman, M.S. & Khater, M.M.A. & Attia, R.A.M. & Baleanu, D., 2020. "Analytical and numerical simulations for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo,Cu)) based on ternary alloys," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Ali, Khalid K. & Nuruddeen, R.I. & Raslan, K.R., 2018. "New structures for the space-time fractional simplified MCH and SRLW equations," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 304-309.
    3. A. Alvarez & F. R. Romero & J. F.R. Archilla & J. Cuevas & P. V. Larsen, 2006. "Breather trapping and breather transmission in a DNA model with an interface," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(1), pages 119-130, May.
    4. Berhe, Hailay Weldegiorgis & Qureshi, Sania & Shaikh, Asif Ali, 2020. "Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    Cited by:

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    2. Xiaoming Wang & Shehbaz Ahmad Javed & Abdul Majeed & Mohsin Kamran & Muhammad Abbas, 2022. "Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    3. Ranković, Dragana & Sivčević, Vladimir & Batova, Anna & Zdravković, Slobodan, 2023. "Three kinds of W-potentials in nonlinear biophysics of microtubules," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Gupta, Vedika & Jain, Nikita & Katariya, Piyush & Kumar, Adarsh & Mohan, Senthilkumar & Ahmadian, Ali & Ferrara, Massimiliano, 2021. "An Emotion Care Model using Multimodal Textual Analysis on COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Zdravković, S. & Zeković, S. & Bugay, A.N. & Petrović, J., 2021. "Two component model of microtubules and continuum approximation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Fokas, A.S. & Cuevas-Maraver, J. & Kevrekidis, P.G., 2020. "A quantitative framework for exploring exit strategies from the COVID-19 lockdown," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Rizvi, Syed T.R. & Seadawy, Aly R. & Farah, N. & Ahmad, S., 2022. "Application of Hirota operators for controlling soliton interactions for Bose-Einstien condensate and quintic derivative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    9. Hussain, Takasar & Aslam, Adnan & Ozair, Muhammad & Tasneem, Fatima & Gómez-Aguilar, J.F., 2021. "Dynamical aspects of pine wilt disease and control measures," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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