The Effects Of Nonstationary Processes On Chaotic And Regular Responses Of The Duffing Oscillator
Abbreviated Journal Title
Int. J. Non-Linear Mech.
This paper deals with the effects of non-stationary regimes on stationary chaotic motions and non-linear attractors: (1) linear variations of the excitation frequency, nu = nu(o) + alpha(v)t, and the amplitude B = B(o) + alpha(B)t; (2) cyclic variations of the excitation frequency, nu = nu(o) + gamma sin alpha(c)t. It was shown in (1) that for very small values of alpha(nu) or alpha(B), i.e. for slow sweeps, the non-stationary responses initially coincide with the stationary chaotic, but then they depart. The faster the sweep, the earlier is the departure from the stationary and from other non-stationary responses. An observation is made that for sufficiently fast sweeps, the initially chaotic motion may be changed into a structured one. In (2) initially stationary chaotic motion is changed instantaneously to another type of motion. The stationary attractors transit into different attractors. Many dynamic phenomena in the real world are modelled mathematically by the non-stationary Duffing differential equation. This paper presents the first attempt to apply non-stationary processes to chaotic motion. It is the objective of this study to contribute to the theory of dynamics and technical design.
International Journal of Non-Linear Mechanics
"The Effects Of Nonstationary Processes On Chaotic And Regular Responses Of The Duffing Oscillator" (1991). Faculty Bibliography 1990s. 293.