Fig. 2: Mathematical solutions of the anharmonic oscillator pair model.

a Numerical solutions over the first four periods, showing that δ(t) varies with the damping coefficients. The selection of the values and physical units is presented in Supplementary information S2. The transient response usually lasts less than two periods. b Steady-state response of δ(t) with different damping coefficients after the automatic correction of the origin, leading to the definition of the phase shift (φx) of the electrostrictive response. c The resulting opening direction of the δ-E parabola also changes from downward to upward. The sign of the electrostrictive coefficient is defined as positive when the deformation is maximum at or after the field is maximum, and negative when the strain is minimum. The change occurs when c = 22.