Dynamical features and sensitivity visualization of thin-film Polarisation equation

Abstract

The present investigation describes the dynamical behavior, multi-stability, and traveling wave solutions of thin-film polarisation equations (TFPE) which describes the propagation of waves in thin-film ferroelectric materials. The extended direct algebraic technique is used to construct the traveling wave patterns. Visual representations of a few randomly selected solutions are provided for physical comprehension. The ordinary differential equation can be expressed in the planar dynamical system using the Galilean transformation. Using various initial conditions for the unperturbed dynamical system, phase portraits with various sorts of trajectories are created. Additionally, the Runge-Kutta method is used to plot nonlinear periodic waves and super nonlinear waves. Additionally, the Hamiltonian function for this undisturbed dynamical system is computed and shown. It also included the source term with amplitude and frequency parameters for the chaotic and quasi-periodic behaviors, and the system is also stated in the non-autonomous form. For the dynamical system under investigation, multi-stability is also thoroughly described. Furthermore, a full inspection of the sensitivity of the perturbed dynamical structure under various initial conditions has been conducted.