Dynamical Analysis of Barium Titanate Crystal in Alternative Voltage RL Circuit

Abstract

This brief paper theoretically investigates the dynamical characteristics of ferroelectric materials, specifically barium titanate $(BaTiO_3) $ crystal in alternative voltage resistor (R) and inductor (L) circuit. The theory of Landau-Ginzburg-Devonshire and Kirchhoff’s law are used to derive the equation for the polarization field in the $ BaTiO_3 $ crystal. The Averaging method is applied to obtain an approximate analytical solution, and the numerical simulations of the system’s equations is used to confirm the analytical obtained solution. The Melnikov method is used to investigate horseshoe chaos and the critical amplitude of excitation. The phase portraits, Poincaré sections, local maxima and greatest Lyapunov exponent are drawn to confirm the results obtained with Melnikov method.