1,068
个编辑
更改
跳到导航
跳到搜索
第55行：
第55行： − One can also consider what happens if one holds b constant and varies a. In the symmetrical case 0}}, one observes a pitchfork bifurcation as a is reduced, with one stable solution suddenly splitting into two stable solutions and one unstable solution as the physical system passes to through the cusp point (0,0) (an example of spontaneous symmetry breaking). Away from the cusp point, there is no sudden change in a physical solution being followed: when passing through the curve of fold bifurcations, all that happens is an alternate second solution becomes available.+ − − 我们也可以考虑，如果一个人保持 b 常数，改变 a 会发生什么。在对称情形0}中，我们观察到 a 被还原时的叉式分岔，当物理系统通过尖点(0,0)时，一个稳定解突然分裂成两个稳定解和一个不稳定解(自发对称性破缺的一个例子)。离开尖点，所遵循的物理解没有突然的变化: 当通过折叠分叉曲线时，所发生的是一个备用的第二解变得可用。
→尖点灾变
One can also consider what happens if one holds ''b'' constant and varies ''a''. In the symmetrical case {{nowrap|''b'' {{=}} 0}}, one observes a [[pitchfork bifurcation]] as ''a'' is reduced, with one stable solution suddenly splitting into two stable solutions and one unstable solution as the physical system passes to {{nowrap|''a'' < 0}} through the cusp point (0,0) (an example of [[spontaneous symmetry breaking]]). Away from the cusp point, there is no sudden change in a physical solution being followed: when passing through the curve of fold bifurcations, all that happens is an alternate second solution becomes available.
One can also consider what happens if one holds ''b'' constant and varies ''a''. In the symmetrical case {{nowrap|''b'' {{=}} 0}}, one observes a [[pitchfork bifurcation]] as ''a'' is reduced, with one stable solution suddenly splitting into two stable solutions and one unstable solution as the physical system passes to {{nowrap|''a'' < 0}} through the cusp point (0,0) (an example of [[spontaneous symmetry breaking]]). Away from the cusp point, there is no sudden change in a physical solution being followed: when passing through the curve of fold bifurcations, all that happens is an alternate second solution becomes available.
我们也可以考虑，如果一个人保持''b''常数，改变''a''会发生什么。在对称情形{{nowrap|''b'' {{=}} 0}}中，我们观察到''a''被还原时的[[叉式分岔]]，当物理系统通过尖点(0,0)时，一个稳定解突然分裂成两个稳定解和一个不稳定解(自发对称性破缺的一个例子)。离开尖点，所遵循的物理解没有突然的变化: 当通过折叠分叉曲线时，所发生的是一个备用的第二解变得可用。