The Study of a Nonlinear Duffing – Type Oscillator Driven by Two Voltage Sources

Abstract

In the present work, a detailed study of a nonlinear electrical oscillator with damping and external excitation is presented. The system under study consists of a Duffing-type circuit driven by two sinusoidal voltage sources having different frequencies. The dynamical behavior of the proposed system is investigated numerically, by solving the system of state equations and simulating its behavior as a circuit using MultiSim. The tools of the theoretical approach are the bifurcation diagrams, the Poincaré sections, the phase portraits, and the maximum Lyapunov exponent. The numerical investigation showed that the system has rich complex dynamics including phenomena such as quasiperiodicity, 3-tori, and chaos.

Keywords

• Nonlinear circuit
• Duffing
• chaos
• quasiperiodicity
• 3-tori
• Poincaré section
• maximum Lyapunov exponent.