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1、精品文档精品文档1. 分岔图:一个耦合发电机系统:混沌动力学行为讨论的程序说明x1 x2x3x1x2 x3x2x1 x3x3x1x2aa耦合系统函数:function dx=ouhe1t,xdx1,1=-x4*x1+x2*x3+x5;dx2,1=-x4*x2+x1*x3-x5; dx3,1=x3-x1*x2;dx4,1=0;dx5,1=0;分岔图程序:clear; clc; Z=;for a=linspace0.5,10.5,500; % 舍弃前面迭带的结果, 用后面的结果画图: 即 0.5-10.5 分为 500点T,Y=ode45ouhe1,1,1;1;1;2;a;T,Y=ode45ouh
2、e1,20,YlengthY,:;Y:,1=Y:,2-Y:,1;for k=2:lengthY f=k-1;if Yk,10y=Yk,2-Yk,1*Yf,2-Yk,2/Yf,1-Yk,1;Z=Z a+absy*i;elseendif Yf,1100lsum=lsum+logd1/d0;endendle=lsum/i-100最大李雅谱指数谱程序:仍对上述耦合系统clear; % 可调参数区间和步长,如a 的第 5 和 36 行clc;LE1=; d0=1e-8;for a=linspace0.5,10.5,300;le=0; lsum=0; x=1; y=1; z=1; x1=1; y1=1;z
3、1=1+d0;for i=1:150T1,Y1=ode45ouhe1,0,1,x;y;z;2;a;T2,Y2=ode45ouhe1,0,1,x1;y1;z1;2;a;n1=lengthY1; n2=lengthY2; x=Y1n1,1;y=Y1n1,2;z=Y1n1,3;x1=Y2n2,1;y1=Y2n2,2;z1=Y2n2,3;d1=sqrtx-x12+y-y12+z-z12; x1=x+d0/d1*x1-x; y1=y+d0/d1*y1-y; z1=z+d0/d1*z1-z;if i50lsum=lsum+logd1/d0;endendendle=lsum/i-50;LE1=LE1 le;
4、a=linspace0.5,10.5,300; plota,LE1,-;titlelargest Lyapunov exponents of ouhe1; xlabelparameter a,ylabellargest Lyapunov exponents; gridnste no px evonupaytLsegral1.210.80.60.40.20-0.2largest Lyapunov exponents of ouhe1024681012parameter a双参数空间的最大李雅谱指数谱程序:仍对以上耦合系统clear; % 可调参数区间和步长clc;global u a N1=li
5、nspace0,0,200; N2=linspace0,0,400; for I=1:200u=1.5+I*0.025; d0=1e-8;for L=1:400a=0.5+L*0.025;le=0; lsum=0; x=1; y=1; z=1; x1=1; y1=1;z1=1+d0;for i=1:150T1,Y1=ode45ouhe1,0,1,x;y;z;u;a;T2,Y2=ode45ouhe1,0,1,x1;y1;z1;u;a;n1=lengthY1; n2=lengthY2; x=Y1n1,1;y=Y1n1,2;z=Y1n1,3;x1=Y2n2,1;y1=Y2n2,2;z1=Y2n2,3
6、;d1=sqrtx-x12+y-y12+z-z12; x1=x+d0/d1*x1-x; y1=y+d0/d1*y1-y; z1=z+d0/d1*z1-z;if i50lsum=lsum+logd1/d0; endendle=lsum/i-50;LE1I,L=le;N2L=a;endN1I=u;endX,Y=meshgridN1,N2;Z=LE1;pcolorX,Y,Z; % 画伪彩图%colormap jet,shading interp % 连续变化的变异饱和色图,表面画伪彩图%contourfX,Y,Z% 画等高线titlelargest Lyapunov exponents of ouh
7、e1 xlabelparameter ituylabelparameter itazlabel 最大李雅普指数 delta,FontSize,1201E-30.20000.30000.40000.50000.60000.70000.80000.90001.0001.1005671.2001086a42234u4. 李雅谱指数程序:仍对以上耦合系统clear;clc; x=1; y=1; z=1;h=0.003; a=3.5;u=2;V=eye3; S=V; b1=0; k=50000;for i=1:kx1=x+h*-u*x+y*z+a; y1=y+h*-u*y+x*z-a; z1=z+h*z
8、-x*y; x=x1;y=y1;z=z1;J=-ua+zyz-a-ux-y-x1;endJ=eye3+h*J; B=J*V*S; V,S,U=svdB;a_max=maxdiagS; S=1/a_max*S; b1=b1+loga_max;Lyapunov=logdiagS+b1/k*h李雅谱指数谱程序:仍对以上耦合系统clear;% 奇特值分解法运算ouhe 系统的李雅普诺夫指数谱clc;Z1=;Z2=;Z3=; x=1; y=1; z=1; h=0.002; u=2;%a=3; k=10000;for a=linspace0.5,10.5,1000; V=eye3;S=V; b1=0;lp
9、=0;for i=1:kx1=x+h*-u*x+y*z+a; y1=y+h*-u*y+x*z-a; z1=z+h*z-x*y; x=x1;y=y1;z=z1;J=-ua+zyz-a-ux-y-x1;J=eye3+h*J; B=J*V*S; V,S,U=svdB;a_max=maxdiagS; S=1/a_max*S; b1=b1+loga_max;endlp=logdiagS+b1/k*h; Z1=Z1 lp1;Z2=Z2 lp2;Z3=Z3 lp3;enda=linspace0.5,10.5,1000; plota,Z1,-,a,Z2,-,a,Z3,-;titleLyapunov expon
10、ents of ouhe; xlabelparameter a,ylabellyapunov exponents; grid onstnpe n ox e v onyu p alLyapunov exponents of ouhe210-1-2-3-4-5024681012parameter a6.三维、二维以准时间序列图: 耦合系统的函数程序:function dx=ouhet,x dx=zeros3,1; a=3;u=2;dx1=-u*x1+x2*x3+a;dx2=-u*x2+x1*x3-a;dx3=x3-x1*x2;图程序: clc; clear;t,x=ode45ouhe,0 1000
11、,1 -1 1;subplot2,2,1; plotx:,1,k,markersize,0.5;xlabelt/ms,fontsize,12,fontName,times new Roman,fontweight,bold,color,k;ylabelx,fontsize,12,fontName,times new Roman,fontweight,bold,color,k;subplot2,2,2; plotx:,2,k,markersize,0.5;xlabelt/ms,fontsize,12,fontName,times new Roman,fontweight,bold,color,k
12、;ylabely,fontsize,12,fontName,times new Roman,fontweight,bold,color,k;subplot2,2,3; plotx:,3,k,markersize,0.5;xlabelt/ms,fontsize,12,fontName,times new Roman,fontweight,bold,color,k;ylabelz,fontsize,12,fontName,times new Roman,fontweight,bold,color,k;subplot2,2,4; plot3x:,1,x:,2,x:,3,k,markersize,0.
13、5;grid on;xlabelx,fontsize,12,fontName,times new Roman,fontweight,bold,color,k;ylabely,fontsize,12,fontName,times new Roman,fontweight,bold,color,k;zlabelz,fontsize,12,fontName,times new Roman,fontweight,bold,color,k;figure2;plot3x:,1,x:,2,x:,3,k,markersize,0.5;grid on; xlabelitxrm_1,fontsize,20,fontName,times new Roman,fontweight,bold,color,k; ylabelitxrm_2,fontsize,20,fontName,times new Roman,fontweight,bold,color,k; zlabelitxrm_3,fontsize,20,fontName,times new Roman,fontweight,bold,color,k;121086420-2-4-615d105x30x 3-5-1020100-10x2-20-2020100-10x1-8020406080100t
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