On asymptotic behavior in cascades chaotically excited non-linear oscillators. (English) Zbl 1235.70171
From the introduction: Because chaotic behavior is structured and, at the same time, possesses elements of uncertainty, we view chaotic response as intermediate between regular (harmonic, periodic, quasi-periodic) and truly random behavior. Furthermore, new examples of chaotic phenomena seem to be emerging continually, and many processes formerly thought to be random may actually be chaotic.
This reinterpretation of seemingly random processes may carry over to the way in which inputs to dynamical systems are modeled. Specifically, we speculate that some external excitations which are difficult a priori to model (such as earthquake excitations of structures or certain fluid-structure interaction problems) may actually be chaotic, not random. Thus, we are led to consider the response of systems to chaotic excitations. In this note we present some (fairly narrowly directed) numerical results of the response of a nonlinear oscillator system to chaotic excitation.
This reinterpretation of seemingly random processes may carry over to the way in which inputs to dynamical systems are modeled. Specifically, we speculate that some external excitations which are difficult a priori to model (such as earthquake excitations of structures or certain fluid-structure interaction problems) may actually be chaotic, not random. Thus, we are led to consider the response of systems to chaotic excitations. In this note we present some (fairly narrowly directed) numerical results of the response of a nonlinear oscillator system to chaotic excitation.
MSC:
70L05 | Random vibrations in mechanics of particles and systems |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
70K40 | Forced motions for nonlinear problems in mechanics |
70K50 | Bifurcations and instability for nonlinear problems in mechanics |
74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |