An Innovative Approach in Inspecting a Damped Mathieu Cubic–Quintic Duffing Oscillator

• DOI: 10.1007/s42417-024-01506-w
• Publication Date: 2024-07-23T17:05:33Z
• Authors: Galal M. Moatimid; Mona A. A. Mohamed; Khaled Elagamy
• Keywords: Duffing equation; Floquet theory; Mathieu function; Parametric oscillator; Quintic function; Ode

Abstract Purpose The objective of the present study is to analyze a damped Mathieu–cubic quintic Duffing oscillator as parametric nonlinear oscillatory dynamical system. This equation has multiple applications in diverse fields, including optics, quantum physics, and general relativity. There are concerns related periodic motion analysis boundary-value problems with elliptic symmetries. current effort aims determine frequency amplitude issues. Method non-perturbative approach (NPA) employed transform ordinary differential (ODE) into linear equation. derivation approximate solutions achieved without relying on typical perturbation approaches, separate from series expansion. Hence, this depart traditional methods acquire approximated for minor components imposing any limitations. Furthermore, technique extended ascertain optimal large fluctuation. Results allows rapid estimation frequency-amplitude relationship order attain successive approximations fluctuations. A validation obtained derived equation, demonstrating high level agreement original An stability behavior conducted scenarios. In addition, Floquet theory used examine transition curves. Conclusion characterized by its clear principles, making it practical, user-friendly, capable achieving exceptionally numerical precision. highly beneficial addressing due ability minimize algebraic complexity during implementation.