论文标题
Mackey-Glass方程中的双重性，分叉和混乱
Bistability, Bifurcations and Chaos in the Mackey-Glass Equation
论文作者
论文摘要
数值分叉分析，尤其是两参数延续，用于与数值模拟的配置中，以揭示Mackey-Glass方程中的复杂动力学，以实现接近混乱发作的延迟的中等值。特别是对周期轨道的尖叉分叉以及周期轨道折叠的产生分支有效地将参数空间划分为看到不同行为的区域。尖叉分叉直接导致周期性轨道之间的双重性，然后在周期性的轨道和混乱的吸引子之间进行双重性。这导致了两种不同的机制，在全球分叉中，在内部危机或边界危机中，混乱的吸引子在全球分叉中被破坏。在参数空间的另一部分中，发现一系列亚临界周期双倍的序列可引起周期轨道和混乱吸引子之间的双重性。还鉴定了圆环分叉和codimension-two-two折叠分叉，并使用Lyapunov指数计算来确定混乱区域和吸引子维度。
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of chaos. In particular a cusp bifurcation of periodic orbits and resulting branches of folds of periodic orbits effectively partition the parameter space into regions where different behaviours are seen. The cusp bifurcation leads directly to bistability between periodic orbits, and subsequently to bistability between a periodic orbit and a chaotic attractor. This leads to two different mechanisms by which the chaotic attractor is destroyed in a global bifurcation with a periodic orbit in either an interior crisis or a boundary crisis. In another part of parameter space a sequence of subcritical period-doublings is found to give rise to bistability between a periodic orbit and a chaotic attractor. Torus bifurcations, and a codimension-two fold-flip bifurcation are also identified, and Lyapunov exponent computations are used to determine chaotic regions and attractor dimension.
