On discontinuous dynamics of a periodically forced double-belt friction oscillator

A new Chebyshev criterion and its application to planar differential systems

“…In this direction there are also some other interesting results, see e.g. [1,10,37] for the models from different real phenomena; and [33] with symmetric rays defined by exp((n + 1)ϑ √ −1) = 1 in ϑ.…”

“…Gasull et al [14] in 2012 studied the first order Melnikov function of the system to obtain the number of limit cycles via the Derivation-Division algorithm. Here we reobtain the result in a simple way by using ECT-system (10).…”

“…We can estimate the number of isolated zeros of M 1 (i.e., M1 ) now. We limit to some number of separation redials, where four of them have appeared in the references [1,4,5,10,29,36,37] (see statements (i)-(iv) of Proposition 19 and Figure 1), and two new ones (statements (v) and (vi)) are added now for the first time, which exhibits some clues that how the maximum number of isolated zeros of M 1 can be affected by the number n and the distribution of the angles ϑ 0 , • • • , ϑ n . Proposition 19.…”

Limit cycles in 4-star-symmetric planar piecewise linear systems

“…Different planar models with f (x, y) = xy can be found in the literature. For example, a model of a steam-engine ( [3]), a periodically forced double-belt friction oscillator ( [13]), or a two-mass model of the human vocal folds used to simulate their oscillatory motion at phonation ( [22]). There are models in higher dimensions, (x 1 , x 2 , .…”

Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law

“…In 2016, Chen and Fan [49] presented the analytical conditions for the motion switchability in a double belt friction oscillator system with a periodic excitation. In 2018, Fan et al [50] further investigated dynamics of such double belt friction oscillator system with a periodic excitation. In 2017 and 2018, Fan et al [51,52] studied a friction-induced oscillator with two degrees of freedom on a speed-varying traveling belt and discontinuous dynamical behaviors in a vibroimpact system with multiple constraints, respectively.…”