Recent results of nonlinear dynamic theories are reviewed and simple nonlinear systems of KDP/RLC circuits driven by external oscillating field, where KDP crystal is near ferroelectric transition, have been experimentally studied. We have been able to observe theoretically predicted nonlinear dynamic transitions in the RLC/KDP circuit. In the nonresonant region, power spectra and return maps of nonlinear dynamic response of $KH_2PO_4$(KDP) crystal near ferroelectric transition temperature $T_c$ in the RLC/KDP circuit are analyzed to confirm Hopf bifurcation, quasiperiodicity and locking. Nonlinear dynamic responses in the RLC/KDP circuit are attributed to the mode coupling between the driven Duffing oscillator mode of the nonlinear polarization and the piezoelectric excitation of the elastic deformation mode. Quasiperiodic signals, observed experimentally in the RLC/KDP circuit, qualitatively agree with the numerical solution of the coupled Duffing oscillator equations of motion which is derived from the Landau potential. Near the region of piezoelectric resonance we observe the frequencyresponse and amplitude-response in the RLC/KDP nonlinear circuit. The experimentally observed hysteresis and jump phenomena are also in qualitative agreement with those of the Duffing oscillator system. In the resonant region, although all the external control parameters in the system remain as fixed, we are able to observe the nonlinear dynamic signals slowly varying in time. We observe the time-dependent torus doubling route with control parameter of varying frequency at the moderate input voltage as confirmed by power spectra and return maps of the sampling signals, obtained from the original time signals. Time-dependent nonlinear dynamic signals, observed in these resonant regions, are similar to those of higher dimensional model systems and spatially extended experimental systems. It seems that such high-dimensional dynamical signals may result from the destruction of coordinated domain wall motion. And its slowly varying time-dependent phenomena seems to be attributed to the characteristics of critical fluctuation dynamics of the system.