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[分形与混沌] 求教一个微分方程组作图的问题

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发表于 2007-4-15 16:04 | 显示全部楼层 |阅读模式

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从一篇论文上看的一个吸引子图,百思不得其解,不知道论文作者是怎么画的,能不能请高人指点一下,只要给我点拨一下怎么做就好,多谢了!
无量纲化以后的方程是这样的:
不明白的是这段文字:
Since the system (4)–(7) describing the particle dynamics
is a periodically forced system, it is natural to consider the
stroboscopic section defined by the time-T map of the flow,
where T is the period of the flow. We denote this map by F.
It is easy to check that if (Y1(t);Y2(t);V1(t);V2(t))
is a solution of Eqs. (4)–(7), then
(Y1(t)+2n;Y2(t)+2m;V1(t);V2(t));
(Y1(t)+1;Y2(t)+1;V1(t);V2(t));
(-Y1(t)+2;Y2(t);-V1(t);V2(t));
(-Y1(t)+1;Y2(t)+1;-V1(t);V2(t));
are also solutions, where m,n are integers. After identifying
all these points with (Y1(t);Y2(t);V1(t);V2(t)), the mapping
F can be regarded as being defined on E=
[0,1]*[0,1]*R*R;   R*R are the velocity components!. We
denote this mapping by F' , in order to distinguish it from F
defined on the whole phase space. In fact, the original dynamics
represented by Eqs. (4)–(7) can also be defined on E,
Then, F'is the time-T mapping of this flow restricted
to E.
Figure 1 shows the projection onto the configuration
space of the chaotic attractor for the mapping F˜ with the
parameter values A=3.2, W=0.8, R=1, k=2.72, omiga=pi
(this means that the forcing period is T=2)
我的问题是:
time-T map怎么画?是画频闪图吗?
如何能画出如下图的吸引子来,虽然无量纲化了Y1,Y2,但求解完之后的Y1,Y2都是大于1的,他这图到底是什么意思啊?
请各位前辈不吝赐教,如有热心的前辈请留下邮箱,我可把全文发过去请教!
多谢了!

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发表于 2007-4-16 04:22 | 显示全部楼层
time-T map怎么画?是画频闪图吗?
如何能画出如下图的吸引子来,虽然无量纲化了Y1,Y2,但求解完之后的Y1,Y2都是大于1的,他这图到底是什么意思啊?
请各位前辈不吝赐教,如有热心的前辈请留下邮箱,我可把全文发过去请教!
多谢了!


time-T map应该就是闪频图

无量纲化未必是到1吧,没仔细看
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