7.分叉与混沌

1、分叉与混沌实验实验目的实验指导px_ := 2 x - 0.001 x2data1 = NestListp, 0, 30ListPlotdata1, PlotStyle -> PointSize0.02Note:横坐标为数据表的位序（索引号）RSolvean + 1 = 2 an - 0.001 an2, a0 = 0, an, n结论：p0=0时，迭代恒等于0，0是迭代的不动点。px_ := 2x - 0.001 x2data1 = NestListp, 1, 30ListPlotdata1, PlotStyle -> PointSize0.02结论：0<p0<100

2、0时，迭代收敛于1000。px_ := 2x - 0.001 x2data1 = NestListp, 1000, 30ListPlotdata1, PlotStyle -> PointSize0.02结论：p0=1000时，迭代恒等于1000，为迭代的不动点。px_ := 2x - 0.001 x2data1 = NestListp, 1500, 30ListPlotdata1, PlotStyle -> PointSize0.02结论：p0>1000时，迭代仍收敛于1000。Note:px_ := 2x - 0.001 x2data1 = NestListp, 1500,

3、 30ListPlotdata1,PlotStyle->PointSize0.02ListPlotdata1,PlotJoined->TrueShow%,%px_:=x+0.002 x (400-x)data=NestListp,2,14ListPlotdata, PlotStyle -> PointSize0.02gx_ := 0.7 x(1 - x);data = NestListg, 0.2, 30;llg1 = ListPlotdata, PlotStyle -> PointSize0.02;llg2 = ListPlotdata, PlotJoined -&g

4、t; True;Showllg1, llg2;g0 = Plotgx, x, x, 0, 1.1, PlotRange -> 0, 1a = 0.2; n = 5;ll = Linea, 0, a, ga;Dob = ga; c = gb;ll = Appendll, Linea, b, b, b,Lineb, b, b, c,Lineb, c, c, c,Linec, c, c, gc;a = c, k, 1, n;g1 = Showg0, Graphicsll;gx_:=2.9(x-x2);data=NestListg,0.2,30;llg1=ListPlotdata,PlotSty

5、le->PointSize0.02;llg2=ListPlotdata,PlotJoined->True;Showllg1,llg2;g0 = Plotgx, x, x, 0, 1.1, PlotRange -> 0, 1a = 0.2; n = 5;ll = Linea, 0, a, ga;Dob = ga; c = gb;ll = Appendll, Linea, b, b, b,Lineb, b, b, c,Lineb, c, c, c,Linec, c, c, gc;a = c, k, 1, n;g1 = Showg0, Graphicsll;gx_:=3.4(x-x

6、2);data=NestListg,0.02,30;llg1=ListPlotdata,PlotStyle->PointSize0.02;llg2=ListPlotdata,PlotJoined->True;Showllg1,llg2;g0 = Plotgx, x, x, 0, 1.1, PlotRange -> 0, 1a = 0.2; n = 5;ll = Linea, 0, a, ga;Dob = ga; c = gb;ll = Appendll, Linea, b, b, b,Lineb, b, b, c,Lineb, c, c, c,Linec, c, c, gc;

7、a = c, k, 1, n;g1 = Showg0, Graphicsll;gx_:=3.55(x-x2);data=NestListg,0.02,30;llg1=ListPlotdata,PlotStyle->PointSize0.02;llg2=ListPlotdata,PlotJoined->True;Showllg1,llg2;g0 = Plotgx, x, x, 0, 1.1, PlotRange -> 0, 1a = 0.2; n = 5;ll = Linea, 0, a, ga;Dob = ga; c = gb;ll = Appendll, Linea, b,

8、 b, b,Lineb, b, b, c,Lineb, c, c, c,Linec, c, c, gc;a = c, k, 1, n;g1 = Showg0, Graphicsll;gx_:=3.70(x-x2);data=NestListg,0.02,30;llg1=ListPlotdata,PlotStyle->PointSize0.02;llg2=ListPlotdata,PlotJoined->True;Showllg1,llg2;g0 = Plotgx, x, x, 0, 1.1, PlotRange -> 0, 1a = 0.2; n = 5;ll = Linea

9、, 0, a, ga;Dob = ga; c = gb;ll = Appendll, Linea, b, b, b,Lineb, b, b, c,Lineb, c, c, c,Linec, c, c, gc;a = c, k, 1, n;g1 = Showg0, Graphicsll;Feign_, x0_ :=Moduleplist = , a, i, temp, pilist = ,Fora = 1, a <= n, a+, temp = x0; plist = ;Fori = 1, i <= 50, i+, temp = 4*a*temp*(1 - temp)/n;Fori = 51, i <= 100, i+, temp = 4*a*temp*(1 - temp)/n;AppendToplist, 4a/n, t