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Zusammenfassung:
The investigation focus here is on the rhythmicity modes transition of stochastic high-order Rayleigh oscillators coupled with impacts and improved memory damping. Preliminarily, the impact constraint in the 10-power configuration Rayleigh model is processed by the mirror image transformation, and then the system response solution on probability distribution is gradually evaluated through the multi-scale expansion, stochastic averaging approach, calculation of the indicators related to Shannon entropy and numerical techniques. Subsequently, the system bifurcation behavior accompanying the rhythmicity modes transition is determined based on changes in system energy on amplitude, the most probable amplitude of the vibrational states, the evolution of the system's spatiotemporal trajectory, and probabilistic trends in joint vibrational response. We describe rhythmicity transition details of the stochastic high-order Rayleigh oscillator by setting up representative parameter scenarios, and the Shannon entropy correlation indices are creatively introduced to quantitatively predict the bifurcation behavior of the system. The theoretical estimates are further confirmed by numerical results, and the intermittent phenomenon displayed in the spatiotemporal evolution sequence of the system states interprets the variation of the half-shaped stochastic attractor modes, indicating the stochastic P-bifurcation, and reflects the transition mechanism of the mono-rhythmicity, bi-rhythmicity and tri-rhythmicity mode of the 10-power Rayleigh oscillator caused by the relevant parameter source. Through a series of perspectives, it checks that the system rhythmicity modes transition manifests strong sensitivity under the high-order Rayleigh damping coefficient change in a small scale, and memory damping factors can significantly regulate the system rhythmicity transition. Concurrently, the apparent change of the indicators related to Shannon entropy provides a quantitative reference for the qualitative analysis of critical transitions within the samples range. Our results provide a new paradigm for control issues in engineering vibration and other interdisciplinary application scenarios.
