一种“类耗散系统”中的“类Ⅴ型阵发”

“Type Ⅴ quasi-intermittency” in a “quasi-dissipative system”

一类不连续不可逆保面积映象可以展示类似耗散的行为 ,因此可称其为“类耗散系统” .在一种类耗散系统中观察到了椭圆周期轨道及其周围的椭圆岛与映象不连续边界碰撞而消失的现象 .周期轨道消失后 ,经过一系列过渡椭圆周期轨道之后 ,系统的行为由一个混沌类吸引子主导 .在混沌类吸引子刚刚出现时 ,混沌时间序列呈现层流相与湍流相的无规交替 .这一切都与不连续耗散系统中发生的Ⅴ型阵发的相应性质十分相似 ,因此可称为“类Ⅴ型阵发” .然而 ,当混沌类吸引子刚刚出现时 ,仅可以找到最后一个过渡椭圆岛的“遗迹” ,并不存在它的“鬼魂” ,因此类Ⅴ型阵发不遵从Ⅴ型阵发的特征标度规律 .反之 ,混沌类吸引子的鬼魂却存在于最后一个过渡椭圆周期轨道的类瞬态过程中 ,因此在类Ⅴ型阵发导致混沌运动的临界点之前 ,由此“类瞬态混沌奇异集”中逃逸的规律就成为标志这一种临界现象的标度律 .这与Ⅴ型阵发又根本不同 .

A kind of discontinuous and noninvertible area preserving maps can display behaviours as a dissipative one, so it may be addressed as a “quasi dissipative system”. In a kind of quasi dissipative systems the disappearance of some elliptic periodic orbits and the elliptic islands around them via a collision with the discontinuous border of the system function can be observed. A chaotic quasi attractor dominates the behaviour of the system after the disappearance of the elliptic periodic orbit,and a sequence of transitional elliptic periodic orbits. When the chaotic quasi attractor just appears, the chaotic time sequence shows a random intersperse between laminar and turbulence phases. All these are very similar to the properties of type Ⅴ intermittency happened in a dissipative system. So, we may call the phenomenon as a “type Ⅴ quasi intermittency”. However, there can be only some remnants of the last disappeared transitional elliptic island instead of its “ghost”, therefore type Ⅴ quasi intermittency does not obey the characteristic scaling laws of type Ⅴ intermittency. On the contrary, the ghost of the chaotic quasi attractor can be found in the quasi transient process of the last transitional elliptic periodic orbit. The scaling law of type Ⅴ quasi intermittency thus becomes the rule for escaping from the “chaotic quasi transient strange set”, which exists before the critical point of the appearance of chaotic motion induced by type Ⅴ quasi intermittency and signifies this critical phenomenon. This is absolutely different from type Ⅴ intermittency.