Nonlinear behaviors as well as the bifurcation mechanism in switched dynamical systems
Nonlinear behaviors as well as the bifurcation mechanism in switched dynamical systems
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DOI：
10.1007/s11071-014-1679-4
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发表时间：
2014-09
影响因子：
5.6
通讯作者：
Ran Zhang;Yu Wang;Zhengdi Zhang;Qinsheng Bi
中科院分区：
文献类型：
--
作者：
Ran Zhang;Yu Wang;Zhengdi Zhang;Qinsheng Bi
建立了具有两种外力矩周期切换的典型离心式飞轮调速器系统的动力学模型，其中状态变量可由两个子系统控制，分别对应于周期激励的自治和非自治系统。在自治子系统中可以观察到两种类型的分叉，其中Hopf分叉可能导致周期振荡的发生，而折叠分叉可能导致平衡点的消失。动力学通常表现为与周期开关具有相同频率的周期振荡，其中切换点可以将轨道的轨迹划分为分别由两个子系统控制的两组分段。在单位周期内观察到与Floquet乘子相关的倍周期分叉的级联，导致系统演化为混沌振荡。此外，由于矢量场的对称性，可以得到两个相互对称的吸引子，它们可以随着参数的变化相互作用而形成一个扩大的吸引子。广义Hopf分叉可能导致周期运动和准周期振动之间的行为交替。
Dynamical model of a typical centrifugal flywheel governor system with periodic switches between two forms of external torque has been established, in which the state variables may be governed by two subsystems corresponding to autonomous and non-autonomous systems with periodic excitation, respectively. Two types of bifurcation can be observed in the autonomous subsystem, where the Hopf bifurcation may lead to the occurrence of periodic oscillation, while the fold bifurcation may result in the disappearance of the equilibrium points. The dynamics often behaves in periodic oscillations with the same frequency as the periodic switch, in which the switching points may divide the trajectory of the orbit into two groups of segments governed by the two subsystems, respectively. Cascading of period-doubling bifurcations related to the Floquet multiplier passing across the unit cycle can be observed, which cause the system to evolve to chaotic oscillations. Furthermore, because of the symmetry of the vector field, two attractors symmetric to each other can be obtained, which may interact with each other to form an enlarged attractor with the variation of the parameters. Generalized Hopf bifurcation may lead to the alternation of the behaviors between periodic movements and quasi-periodic oscillations.