کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4610442 | 1338563 | 2014 | 49 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Global Hopf bifurcation of differential equations with threshold type state-dependent delay Global Hopf bifurcation of differential equations with threshold type state-dependent delay](/preview/png/4610442.png)
We develop global Hopf bifurcation theory of differential equations with state-dependent delay using the S1S1-equivariant degree and investigate a two-degree-of-freedom mechanical model of turning processes. For the model of turning processes we show that the extreme points of each vibration component of the non-constant periodic solutions can be embedded into a manifold with explicit algebraic expression. This observation enables us to establish analytical upper and lower bounds of the amplitudes of the periodic solutions in terms of the system parameters and to exclude certain periods. Using the achieved global bifurcation theory we reveal that if the relative frequency between the natural frequency and the turning frequency varies in a certain interval, then generically every bifurcated continuum of periodic solutions must terminate at a bifurcation point. This termination means that the underlying system with parameters in the stability region near the vertical asymptotes of the stability lobes is less subject to chatter. In the process, several sufficient conditions for the non-existence of non-constant periodic solutions are also obtained.
Journal: Journal of Differential Equations - Volume 257, Issue 7, 1 October 2014, Pages 2622–2670