Harmonic Solutions Analysis and Floquet Theory in a Nonlinear Dissipative Hybrid Oscillator | Chapter 8 | Novel Research Aspects in Mathematical and Computer Science Vol. 5

The major goal is to investigate how the traditional Rayleigh-Duffing oscillator is modified by the novel nonlinear cubic, pure quadratic, and hybrid dissipative components. Similar to this, depending on their field of application, the parameters included are utilised to impose a regular, quasi-periodic, or even chaotic behaviour on the systems depicted by this oscillator. We study hysteresis, quasiperiodicity, and chaoticity in a nonlinear dissipative hybrid oscillator. A modified Rayleigh-Duffing oscillator will be used. The traditional Rayleigh-Duffing oscillator is modified by the novel nonlinear cubic, pure quadratic, and hybrid dissipative components at the same time. A detailed investigation of how each of these novel parameters affects the oscillator's dynamics has produced some surprising findings. It is obvious that any of these novel dissipation factors may be employed to modify the oscillator's dynamics. Hysteresis, amplitude jump, and resonance phenomena may be exploited to minimise or eliminate them in some cases, while they may be amplified in others. These new parameters can also be used to force a regular, quasi-periodic, or even chaotic behaviour on the systems represented by this oscillator, depending on their area of use. One of the early findings is the equation of the curve defining the zone of instability of the harmonic oscillation amplitudes. In order to regulate and anticipate the loss or gain of energy during this jump, it is therefore feasible to know the zone of amplitude authorised or the amplitude leap for the systems using this equation. The second stability of the system's oscillations is investigated, along with the impact of the dissipation parameters on this stability, it is concluded. It is important to keep in mind that the effect of certain of these characteristics relies on their coexistence.

Author (s) Details:

A. V. Monwanou,
Institut de Math´ematiques et de Sciences Physiques, Universit´e d’Abomey-Calavi, Benin.

C. H. Miwadinou,
Ecole Normale Sup´erieure de Natitingou, Universit´e d’Abomey, Benin.

C. Ainamon,
Institut de Math´ematiques et de Sciences Physiques, Universit´e d’Abomey-Calavi, Benin.

J. B. Chabi Orou,
Institut de Math´ematiques et de Sciences Physiques, Universit´e d’Abomey-Calavi, Benin.

Please see the link here: https://stm.bookpi.org/NRAMCS-V5/article/view/7485