Tri-Coupled Bidirectional Duffing Oscillators: Applications of Fractional Calculus in Nonlinear Dynamics

Resumen

In recent years, the Duffing Oscillator has been extensively applied to model a variety of physical and biological phenomena. The study of chaotic oscillators often necessitates the use of fractional calculus, as Caputo's definition enables the modeling and numerical implementation of systems that do not conform strictly to integer-order derivatives. In this work, fractional calculus was incorporated into a tri-coupled, bidirectional Duffing Oscillator to analyze its dynamics under varying conditions. The investigation focused on temporal responses and the identification of chaotic attractors as coupling parameters and fractional derivative orders were adjusted. Numerical methods were employed to solve the proposed model, and the dynamics were explored through phase plane analysis, time series, and bifurcation diagrams. The findings provide key insights into the behavior of the system across different parameter regimes.