强迫的Oregonator振子混沌维数与立方映象

CHAOTIC DIMENSIONS OF FORCED OREGONATOR OSCILLATOR AND CUBIC MAP

本文论证了强迫的Oregonator振子可以用立方映象刻划其行为,其依据为描述此振子的四变量方程有三个不动点,混沌的转换函数呈现三次曲线特点,找到了隶属三点周期的符号BK;C,四点周期的符号BK;LC,B^2K;C,BRK;C,并画出了BRK;C的环状线,找到了一条倍周期分岔道路。在混沌域中研究了五个混沌态,其维数介于2.02—2.37之间,混沌域中央维数偏低,贴近四点周期线维数偏高。

In this paper, we prove that forced Oregonator oscillator may be describled by cubic map, for there are three fixed points in four variables differential equations and the transfer function of chaos represents the character of cubic curve. We find the DSP symbolic description of 3-point cycle BK; C, 4-point cycle BK; LC, BK; C, BRK; C and draw a cycle line of BRK; C. We find two of one type in period-doubling bifurcations along a straight line. We studied five chaotic behaviours. Its dimensions are 2.02-2.37. In the middle region of chaos, its dimensions are slightly smaller, i.e., 2.02 to 2.09. Near the 4-point cycle line, its dimensions are 2.16 to 2.34.