arXiv subjects

Yuyi Zhang

Publications and source records attributed to Yuyi Zhang.

20 records · Page 2Linked to original sources

arXiv2021

Switch System with Stable Period Orbit

Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates between unstable modes with the same period orbit, but exhibits stability for fast-switching frequencies and converges to the period orbit. Through mathematical analysis, we elucidate the stabilization mechanism and construct a general class of unstable systems that can form stable switched systems. The demonstration of this new system with period orbit provide a new sight in the study of switched system.

math.DS↗

arXiv2019

On the transformations linearizing isochronous centers of Hamiltonian systems

In this paper we study the transformations linearizing isochronous centers of planar Hamiltonian differential systems with polynomial Hamiltonian functions $H(x,y)$ having only isolated singularities. Assuming the origin is an isochronous center lying on the level curve $L_0$ defined by $H(x,y)=0$, we prove that, there exists a canonical linearizing transformation analytic on a simply-connected open set $Ω$ with closure $\overlineΩ=\mathbb{R}^2$, if and only if, $L_0$ consists of only isolated points; furthermore, if the origin is the unique center, then the condition that $L_0$ consists of only isolated points implies that the corresponding canonical linearizing transformation can be analytically defined on the whole plane.

math.CA↗