ANALYSIS OF CLASS OF NONLINEAR-SYSTEM UNDER DETERMINISTIC AND STOCHASTIC EXCITATIONS

In this paper, some analysis techniques of nonlinear dynamics are appl ied to physical systems which may be modeled by the Duffing nonlinear differential equation. The response of the Duffing oscillator to both deterministic sinusoidal and stochastic loadings is investigated and d istinct regimes of the response motion are discerned and discussed. Th e stochastic input to the system is low-pass Gaussian white noise. The efficacy of studying the variation in time of the probability density of one or more of the system output states to determine the type of m otion of the system is examined. Attractors in phase space are defined via Poincare mapping and bounds on motion which serve as signatures f or particular types of motion (e.g., chaotic, periodic) are identified by a hypervolume measurement technique. An accepted method for adapti ng one measured output state into a higher dimensional space by using time-delayed coordinates is used in conjunction with correlation dimen sion calculation to supply a lower-bound estimate of the fractal dimen sion and insight into the character of the motion of a nonlinear dynam ic system.