Chaotic dynamics in simple nonlinear systems

Abstract

Results of recent studies in nonlinear dynamics are briefly reviewed and two nonlinear systems have been experimentally studied and discussed : A KDP crystal driven by external oscillating field near ferroelectric transition and a coupled nonlinear electronic oscillator. We have been able to observe most of the theoretically predicted nonlinear transitions in the above two systems. Though the phase locking and the quasiperiodicity routes to chaos were the characteristic nonlinear transition observed in KDP crystal, period doubling cascades and intermittencies were also easily observed. Nonlinear transitions in KDP crystal are attributed to the nonlinear couplings between the polarization modes and the shear modes. Those phenomena were qualitatively explained by the coupled motions in Landau potential. We have first succeeded to observe the type-Il intermittency in a coupled nonlinear oscillator circuit. The experimental data such as time sequences, Poincare sections, return maps and the average lengths of the laminar periods are in good agreement with the theoretical results of simple standard models.