To apply effective methods to analyze and distinguish all kinds of response patterns is an important issue of nonlinear dynamics. This paper contributes to develop an alternative Poincaré section method to analyze and identify the whirl responses of a nonlinear oscillator. This integration for analyzing high-order harmonic and chaotic motions is used to integrate the distance between state traj...

Accurately predicting the onset of large behavioral deviations associated with saddlenode bifurcations is imperative in a broad range of sciences and for a wide variety of purposes, including ecological assessment, signal amplification, and microscale mass sensing. In many such practices, noise and non-stationarity are unavoidable and everpresent influences. As a result, it is critical to simul...

Mass-spring models are essential for the description of sloshing resonances in engineering. By experimentally measuring liquid's centre mass a horizontally oscillated rectangular tank, we show that low-amplitude obeys Duffing equation. A bending response curve analogy to softening spring is observed, with growing hysteresis as driving amplitude increases. At large amplitudes, complex wave patte...