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求助利用matlab胞映射法绘制非线性动力学方程的吸引域程序？

作者 逍遥子7777: 来源: 小木虫 500 10 举报帖子

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其中除了x,y是变量其他的都是能赋值的参数，求大神指点，或者杜芬振子的吸引域参考程序？

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独孤神宇

这里面 t 是变量还是传递参数?

你这是需要绘制x(t),y(t)亦或是y(x)等等均需要求解微分方程组
逍遥子7777

你好，里面的时间是参数，可以给一个变化范围，比如t=0:0.1:2000;里面的参数可以取值为u=0.1,f=1,beta1=1,beta2=1,w=1,p=0.2,gama=0.06,gama1=0.05,gama2=0.05,初值可以取为【0,0,0,0】，请问这吸引域是需要用什么方式编写程序啊？
逍遥子7777

引用回帖:
2楼: Originally posted by 独孤神宇 at 2018-05-21 16:44:42
这里面 t 是变量还是传递参数?

你这是需要绘制x(t),y(t)亦或是y(x)等等均需要求解微分方程组

x,y都是关于时间t的函数，最后需要求的是x'与x之间的关系
逍遥子7777

引用回帖:
2楼: Originally posted by 独孤神宇 at 2018-05-21 16:44:42
这里面 t 是变量还是传递参数?

你这是需要绘制x(t),y(t)亦或是y(x)等等均需要求解微分方程组

里面的x,y是随时间变化的变量，最后需要求的是x与x'的关系
逍遥子7777

引用回帖:
2楼: Originally posted by 独孤神宇 at 2018-05-21 16:44:42
这里面 t 是变量还是传递参数?

你这是需要绘制x(t),y(t)亦或是y(x)等等均需要求解微分方程组

求大神知道一下
独孤神宇

引用回帖:
6楼: Originally posted by 逍遥子7777 at 2018-05-21 17:02:28
求大神知道一下...

你这个实际上就是解微分方程组，求得x和x'，下面是用 1stOpt 求解的。

Code :

Variable t[0:0.1:200],x=0,x'=0,y=0,y'=0;
Constant u=0.1,f=1,beta1=1,beta2=1,w=1,p=0.2,gama=0.06,gama1=0.05,gama2=0.05;
Plot  x'[x],x;
ODEFunction  x''=-u*gama1*x'-gama*x'+gama2*f*y'+(u+1)*x-(u+1)*beta1*x^3-f^2*y+f^2*beta2*y^3;
         y''=-gama2*f*y'+u*gama1*x'+f^2*y-f^2*beta2*y^3-u*x+u*beta1*x^3+p*cos(w*t);

结果见图
*********************************

你这个点数太多了,下面是 t=0:0.1:2 的数据：

ODE Functions(Initial Value Problem - IVP):
1: x' = dx/dt = x'
2: x'' = dx'/dt = -0.1*0.05*x'-0.06*x'+0.05*1*y'+(0.1+1)*x-(0.1+1)*1*x^3-1^2*y+1^2*1*y^3
3: y' = dy/dt = y'
4: y'' = dy'/dt = -0.05*1*y'+0.1*0.05*x'+1^2*y-1^2*1*y^3-0.1*x+0.1*1*x^3+0.2*cos(1*t)
Method: Runge-Kutta-Fehlberg Method
Step size: 0.1
Step No.: 20
Results:
t x(t) x'(t) y(t) y'(t)
x'(t) x''(t) y'(t) y'
'(t)
0 0 0 0 0
0 0 0 0.
2
2 -0.127945396227316 -0.270910990899219 0.398548910630361 0.4119584
59403202 -0.270910990899219 -0.435471792076159 0.411958459403202 0.
242646157253493
Results Process:
t x(t) x'(t) y(t) y'(t)
x'(t) x''(t) y'(t) y'
'(t)
0 0 0 0 0
0 0 0 0.
2
0.1 8.31083873035914E-7 1.65984804941913E-5 0.000998334924557777 0.0199500
599302625 1.65984804941913E-5 -9.95642003347977E-7 0.0199500599302625 0.
199001663872652
0.2 -5.13353337339394E-9 -6.6518296332068E-5 0.00398669066625572 0.0398005
174844853 -6.6518296332068E-5 -0.0019922833863813 0.0398005174844853 0.
198009584918876
0.3 -2.24206453787723E-5 -0.000448127803410613 0.00895516357955666 0.0595528
41035504 -0.000448127803410613 -0.0059723377715261 0.059552841035504 0.
197044102619484
0.4 -0.00010623181459192 -0.00132788765959999 0.0158941326729252 0.0792115
544026309 -0.00132788765959999 -0.011960082018967 0.0792115544026309 0.
196145722265727
0.5 -0.000311347841726199 -0.00290831563938813 0.0247946632242499 0.0987861
638003365 -0.00290831563938813 -0.0199935539632451 0.0987861638003365 0.
195373217468138
0.6 -0.00071814982963336 -0.00539662436626998 0.0356490924081482 0.1182928
63413318 -0.00539662436626998 -0.0301283281320792 0.118292863413318 0.
194801099116736
0.7 -0.00142804498574229 -0.00900638476842817 0.0484517717597626 0.1377559
55812331 -0.00900638476842817 -0.0424356611113807 0.137755955812331 0.
194516439580872
0.8 -0.00256417736248466 -0.0139589877133777 0.0631999346876795 0.1572089
21189073 -0.0139589877133777 -0.0570002957947794 0.157208921189073 0.
194615016424011
0.9 -0.00427227308840459 -0.020484864705282 0.0798946504156021 0.1766950
64208579 -0.020484864705282 -0.0739178156693435 0.176695064208579 0.
195196706096273
1 -0.00672159349101865 -0.0288244146918211 0.0985418181954977 0.1962676
5820834 -0.0288244146918211 -0.0932913777882234 0.19626765820834 0.
19636001403272
1.1 -0.010105963227501 -0.0392285627921731 0.119153146953792 0.2159894
92488492 -0.0392285627921731 -0.115227566439718 0.215989492488492 0.
198195573391867
1.2 -0.0146448316475197 -0.051958845319283 0.141747055165749 0.2359317
08564531 -0.051958845319283 -0.139830990520822 0.235931708564531 0.
200778381380859
1.3 -0.0205843129149257 -0.0672868700695973 0.166349413070598 0.2561717
84692771 -0.0672868700695973 -0.167197085318587 0.256171784692771 0.
204158472193045
1.4 -0.0281981322767958 -0.0854929364880343 0.192994033645809 0.2767904
94273609 -0.0854929364880343 -0.19740235982278 0.276790494273609 0.
208349653627744
1.5 -0.0377883800798375 -0.106863510444223 0.221722799340196 0.2978676
23049344 -0.106863510444223 -0.230491037220233 0.297867623049344 0.
21331586845888
1.6 -0.049685938745903 -0.131687124708051 0.252585287773255 0.3194761
83549753 -0.131687124708051 -0.266456651353511 0.319476183549753 0.
218954694934621
1.7 -0.0642503970695685 -0.160248108888451 0.285637730993335 0.3416748
15931969 -0.160248108888451 -0.305216671580801 0.341674815931969 0.
225077495118474
1.8 -0.0818691959857064 -0.192817330800153 0.320941109421449 0.3644980
17895356 -0.192817330800153 -0.346577630710699 0.364498017895356 0.
231385789262554
1.9 -0.102955654416883 -0.229638845192835 0.35855814402855 0.3879438
12664922 -0.229638845192835 -0.390187551808285 0.387943812664922 0.
237443630950968
2 -0.127945396227316 -0.270910990899219 0.398548910630361 0.4119584
59403202 -0.270910990899219 -0.435471792076159 0.411958459403202 0.
242646157253493

TIM截图20180521194507.jpg

，
独孤神宇

引用回帖:
5楼: Originally posted by 逍遥子7777 at 2018-05-21 17:00:56
里面的x,y是随时间变化的变量，最后需要求的是x与x'的关系...

matlab 求解二阶微分方程组的例子还是挺多的，网上可以搜搜。。

http://www.ilovematlab.cn/thread-335348-1-1.html