An Innovative Methodology in Analyzing Some Coupled Dynamical System Linked With Duffing Oscillators

Gamal M. Ismail, Galal M. Moatimid, Y. Y. Ellabban and Mohra Zayed

Journal of Mathematics, 2025, vol. 2025, 1-16

Abstract: Innovative methodologies are being studied in analyzing coupled dynamical systems (2DOF) with Duffing oscillators (DOs), which model various real-world phenomena. These methods reveal concealed dynamics, improve chaotic response prediction, and provide deeper insight into organization and bifurcation structures. The linked technique is highly effective of all initial amplitudes and accurately computes higher-order approximations. The non-perturbative approach (NPA) is functional as a novel methodology. This method successfully transforms the weakly oscillator of nonlinear ordinary differential equations (ODEs) into linear ones. The Mathematica Software (MS) is utilized to validate the precision of the numerical solution (NS) of the pertinent systems. Additionally, Tabular means are used to confirm the results. The NPA principally depends on He’s formulation formula (HFF) as its fundamental basis. The distinct methodology can be employed of diverse classifications of individual or coupled nonlinear dynamic systems. Despite the use of several perturbation procedures, the NPA successfully overcomes the constraints related to the application of restoring forces in the equations of motion (EOMs). Moreover, the NPA enables us to analyze the stability criteria of the system being studied. Thereby, the NPA serves as a more effective accountability instrument in examining NS approximations of highly weakly nonlinear oscillators. The NPA can be easily modified to address many nonlinear categories, rendering it a significant tool in technology and applied science disciplines.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1896211

DOI: 10.1155/jom/1896211

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