Dynamical Analysis of Barium Titanate Crystal in Alternative Voltage RL Circuit

This brief paper theoretically investigates the dynamical characteristics of ferroelectric materials,specifically barium titanate(BaTiO3)crystal in alternative voltage resistor (R) and inductor (L) circuit. Thetheory of Landau-Ginzburg-Devonshire and Kirchhoff’s law are used to derive the equation for the polarizationfield in theBaTiO3crystal. The Averaging method is applied to obtain an approximate analytical solution, andthe numerical simulations of the system’s equations is used to confirm the analytical obtained solution. TheMelnikov method is used to investigate horseshoe chaos and the critical amplitude of excitation. The phaseportraits, Poincaré sections, local maxima and greatest Lyapunov exponent are drawn to confirm the resultsobtained with Melnikov method.