Ball R, Dewar RL
Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physical Sciences & Engineering, The Australian National University, Canberra 0200 Australia.
Phys Rev Lett. 2000 Apr 3;84(14):3077-80. doi: 10.1103/PhysRevLett.84.3077.
Two dynamical models that have been proposed to describe transitions between low- and high-confinement states in confined plasmas are analyzed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.
利用奇点理论和稳定性理论分析了两个为描述约束等离子体中低约束态和高约束态之间转变而提出的动力学模型。结果表明，定态分岔集具有与叉形分岔和转临界分岔的标准范式相同的定性性质。该分析得出了最高阶奇点的余维数，据此我们发现未受扰动的系统是超定分岔问题，并推导了适当的通用展开式。文中讨论了相互等价性问题以及状态转变的特征。
