一类具有两个边界的分段光滑系统中边界碰撞分岔现象及混沌

以不连续运行模式下的电流反馈型Buck-Boost变换器为例，导出了一类具有三段形式的分段光滑迭代映射方程，数值仿真得到了输入电压变化时的分岔图.结果表明，发生分岔时映射雅可比矩阵的特征值以不连续的方式跳跃出复平面上的单位圆，而且映射总有某个或某些轨道点位于相平面中不同区域的边界上，即映射随输入电压的变化会发生边界碰撞分岔现象，如由周期态到周期态以及由周期态到混沌态的分岔. 关键词： 分段光滑系统 边界碰撞分岔 混沌

Border collision bifurcations and chaos in a class of piecewise smooth systems w ith two boundaries

A class of piecewise smooth maps with three zones is derived to describe the dynamics of a current-programmed Buck-Boost converter operating in a discontinuous mode. The numerical simulation is carried out and the bifurcation diagrams w ith the input voltage as a parameter are obtained. It is shown that, when a bifu rcation occurs, some eigenvalues of the Jacobian matrix jumps over the unit circ le in a discontinuous way, and there are always some orbit points lying on the b oundaries which separate different regions in the phase plane. It is concluded t hat border collision bifurcations could occur when the input voltage varies, for example, a bifurcation from a periodic orbit to another periodic orbit or chaot ic orbit.