Analysis of Multiresonance and Chaotic Behavior of the Polarization in Materials Modeled by a Duffing Equation with Multifrequency Excitations

Abstract

This paper considers nonlinear dynamics of polarization oscillations when some materials are subjected to the action of an electromagnetic wave modeled by multifrequency forced Duffing equation. Multiresonance and chaotic behavior are analyzed. For the resonance analysis, the method of multiple scales is used. The phenomena of amplitude jump and hysteresis for polarization were observed and analyzed. Finally, the study of chaotic behavior for polarization was made by numerical simulation using the Runge-Kutta fourth order algorithm.