Dynamics and stability analysis of nonlinear DNA molecules: Insights from the Peyrard-Bishop model

Mostafa M. A. Khater; Mohammed Zakarya; Kottakkaran Sooppy Nisar; Abdel-Haleem Abdel-Aty; Mostafa M. A. Khater; Mohammed Zakarya; Kottakkaran Sooppy Nisar; Abdel-Haleem Abdel-Aty

doi:10.3934/math.20241140

AIMS Mathematics

2024, Volume 9, Issue 9: 23449-23467. doi: 10.3934/math.20241140

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Dynamics and stability analysis of nonlinear DNA molecules: Insights from the Peyrard-Bishop model

1.
School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, PR China
2.
Institute of Digital Economy, Ugra State University, Khanty-Mansiysk, Russia
3.
Department of Basic Sciences, High Institute for Engineering and Technology Al Obour, Cairo 11828, Egypt
4.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
5.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
6.
Department of Physics, College of Sciences, University of Bisha, Bisha 61922, Saudi Arabi

Received: 30 January 2024 Revised: 18 June 2024 Accepted: 05 July 2024 Published: 05 August 2024
MSC : 35C08, 35Q05, 92C40, 70H06

This study explores the nonlinear Peyrard-Bishop DNA dynamic model, a nonlinear evolution equation that describes the behavior of DNA molecules by considering hydrogen bonds between base pairs and stacking interactions between adjacent base pairs. The primary objective is to derive analytical solutions to this model using the Khater Ⅲ and improved Kudryashov methods. Subsequently, the stability of these solutions is analyzed through Hamiltonian system characterization. The Peyrard-Bishop model is pivotal in biophysics, offering insights into the dynamics of DNA molecules and their responses to external forces. By employing these analytical techniques and stability analysis, this research aims to enhance the understanding of DNA dynamics and its implications in fields such as drug design, gene therapy, and molecular biology. The novelty of this work lies in the application of the Khater Ⅲ and an enhanced Kudryashov methods to the Peyrard-Bishop model, along with a comprehensive stability investigation using Hamiltonian system characterization, providing new perspectives on DNA molecule dynamics within the scope of nonlinear dynamics and biophysics.
- Peyrard-Bishop model,
- DNA dynamics,
- nonlinear evolution equations,
- analytical solutions
Citation: Mostafa M. A. Khater, Mohammed Zakarya, Kottakkaran Sooppy Nisar, Abdel-Haleem Abdel-Aty. Dynamics and stability analysis of nonlinear DNA molecules: Insights from the Peyrard-Bishop model[J]. AIMS Mathematics, 2024, 9(9): 23449-23467. doi: 10.3934/math.20241140

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Abstract

This study explores the nonlinear Peyrard-Bishop DNA dynamic model, a nonlinear evolution equation that describes the behavior of DNA molecules by considering hydrogen bonds between base pairs and stacking interactions between adjacent base pairs. The primary objective is to derive analytical solutions to this model using the Khater Ⅲ and improved Kudryashov methods. Subsequently, the stability of these solutions is analyzed through Hamiltonian system characterization. The Peyrard-Bishop model is pivotal in biophysics, offering insights into the dynamics of DNA molecules and their responses to external forces. By employing these analytical techniques and stability analysis, this research aims to enhance the understanding of DNA dynamics and its implications in fields such as drug design, gene therapy, and molecular biology. The novelty of this work lies in the application of the Khater Ⅲ and an enhanced Kudryashov methods to the Peyrard-Bishop model, along with a comprehensive stability investigation using Hamiltonian system characterization, providing new perspectives on DNA molecule dynamics within the scope of nonlinear dynamics and biophysics.

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