如何用Matlab绘出广义Lorenz系统规范式的图形？请高手指教 针对lorenz系统的研究有哪些
\u5229\u7528matlab\u505a\u51fa\u6d1b\u4f26\u8328\uff08Lorenz\uff09\u65b9\u7a0b\u7684\u56fe\u50cf\u8c03\u7528ODE45\u6765\u89e3\u7b97\u5e38\u5fae\u5206\u65b9\u7a0b\u5c31\u884c
\u5177\u4f53\u4f60\u53ef\u4ee5\u770b\u4e0bmatlab\u7684ode45\u547d\u4ee4\u7684\u5e2e\u52a9
\u3000\u3000\u7f57\u5170\u897f(Lorenz)\uff0c\u610f\u5927\u5229\u5927\u4f17\u54c1\u724c\u3002\u3000\u3000\u7531\u4e8e\u5728\u949f\u8868\u5e02\u573a\u7684\u51fa\u8272\u8868\u73b0\uff0cLORENZ\u5f97\u5230\u4e86\u5e94\u6709\u7684\u8363\u8a89\u30022003\u5e749\u6708\uff0c\u7531\u7c73\u5170\u7701\u5546\u65c5\u8054\u76df\u63d0\u540d\uff0cLORENZ\u88ab\u5f53\u5730\u7684\u5de5\u5bb6\u5546\u8054\u5408\u4f1a\u6388\u4e88\u201c\u7c73\u5170\u5386\u53f2\u4f01\u4e1a\u201d\u79f0\u53f7\u3002
由MATLAB自带的Demo修改了一个，供参考。
关于广义Lorenz系统规范式，参见百度文库：
http://wenku.baidu.com/view/94de6f35ee06eff9aef8071f.html
方程在最后面的函数lorenzeq
function GLCF(action)
% 广义Lorenz系统规范式，由MATLAB自带Demo修改而来
% 参见百度文库：
%
% 方程在最后面的函数lorenzeq
% Information regarding the play status will be held in
% the axis user data according to the following table:
play= 1;
stop=-1;
if nargin<1,
action='initialize';
end;
if strcmp(action,'initialize'),
oldFigNumber=watchon;
figNumber=figure( ...
'Name','Lorenz Attractor', ...
'NumberTitle','off', ...
'Visible','off');
colordef(figNumber,'black')
axes( ...
'Units','normalized', ...
'Position',[0.05 0.10 0.75 0.95], ...
'Visible','off');
text(0,0,'Press the "Start" button to see the Lorenz demo', ...
'HorizontalAlignment','center');
axis([-1 1 -1 1]);
%===================================
% Information for all buttons
labelColor=[0.8 0.8 0.8];
yInitPos=0.90;
xPos=0.85;
btnLen=0.10;
btnWid=0.10;
% Spacing between the button and the next command's label
spacing=0.05;
%====================================
% The CONSOLE frame
frmBorder=0.02;
yPos=0.05-frmBorder;
frmPos=[xPos-frmBorder yPos btnLen+2*frmBorder 0.9+2*frmBorder];
h=uicontrol( ...
'Style','frame', ...
'Units','normalized', ...
'Position',frmPos, ...
'BackgroundColor',[0.50 0.50 0.50]);
%====================================
% The START button
btnNumber=1;
yPos=0.90-(btnNumber-1)*(btnWid+spacing);
labelStr='Start';
cmdStr='start';
callbackStr='lorenz(''start'');';
% Generic button information
btnPos=[xPos yPos-spacing btnLen btnWid];
startHndl=uicontrol( ...
'Style','pushbutton', ...
'Units','normalized', ...
'Position',btnPos, ...
'String',labelStr, ...
'Interruptible','on', ...
'Callback',callbackStr);
%====================================
% The STOP button
btnNumber=2;
yPos=0.90-(btnNumber-1)*(btnWid+spacing);
labelStr='Stop';
% Setting userdata to -1 (=stop) will stop the demo.
callbackStr='set(gca,''Userdata'',-1)';
% Generic button information
btnPos=[xPos yPos-spacing btnLen btnWid];
stopHndl=uicontrol( ...
'Style','pushbutton', ...
'Units','normalized', ...
'Position',btnPos, ...
'Enable','off', ...
'String',labelStr, ...
'Callback',callbackStr);
%====================================
% The INFO button
labelStr='Info';
callbackStr='lorenz(''info'')';
infoHndl=uicontrol( ...
'Style','push', ...
'Units','normalized', ...
'position',[xPos 0.20 btnLen 0.10], ...
'string',labelStr, ...
'call',callbackStr);
%====================================
% The CLOSE button
labelStr='Close';
callbackStr='close(gcf)';
closeHndl=uicontrol( ...
'Style','push', ...
'Units','normalized', ...
'position',[xPos 0.05 btnLen 0.10], ...
'string',labelStr, ...
'call',callbackStr);
% Uncover the figure
hndlList=[startHndl stopHndl infoHndl closeHndl];
set(figNumber,'Visible','on', ...
'UserData',hndlList);
watchoff(oldFigNumber);
figure(figNumber);
elseif strcmp(action,'start'),
axHndl=gca;
figNumber=gcf;
hndlList=get(figNumber,'UserData');
startHndl=hndlList(1);
stopHndl=hndlList(2);
infoHndl=hndlList(3);
closeHndl=hndlList(4);
set([startHndl closeHndl infoHndl],'Enable','off');
set(stopHndl,'Enable','on');
% ====== Start of Demo
set(figNumber,'Backingstore','off');
% The graphics axis limits are set to values known
% to contain the solution.
set(axHndl, ...
'XLim',[0 40],'YLim',[-35 10],'ZLim',[-10 40], ...
'Userdata',play, ...
'XTick',[],'YTick',[],'ZTick',[], ...
'Drawmode','fast', ...
'Visible','on', ...
'NextPlot','add', ...
'Userdata',play, ...
'View',[-37.5,30]);
xlabel('X');
ylabel('Y');
zlabel('Z');
% The orbit ranges chaotically back and forth around two different points,
% or attractors. It is bounded, but not periodic and not convergent.
% The numerical integration, and the display of the evolving solution,
% are handled by the function ODE23P.
FunFcn='lorenzeq';
% The initial conditions below will produce good results
%y0 = [20 5 -5];
% Random initial conditions
y0(1)=rand*30+5;
y0(2)=rand*35-30;
y0(3)=rand*40-5;
t0=0;
tfinal=100;
pow = 1/3;
tol = 0.001;
t = t0;
hmax = (tfinal - t)/5;
hmin = (tfinal - t)/200000;
h = (tfinal - t)/100;
y = y0(:);
tau = tol * max(norm(y,'inf'),1);
% Save L steps and plot like a comet tail.
L = 50;
Y = y*ones(1,L);
cla;
head = line( ...
'color','r', ...
'Marker','.', ...
'markersize',25, ...
'erase','xor', ...
'xdata',y(1),'ydata',y(2),'zdata',y(3));
body = line( ...
'color','y', ...
'LineStyle','-', ...
'erase','none', ...
'xdata',[],'ydata',[],'zdata',[]);
tail=line( ...
'color','b', ...
'LineStyle','-', ...
'erase','none', ...
'xdata',[],'ydata',[],'zdata',[]);
% The main loop
while (get(axHndl,'Userdata')==play) & (h >= hmin)
if t + h > tfinal, h = tfinal - t; end
% Compute the slopes
s1 = feval(FunFcn, t, y);
s2 = feval(FunFcn, t+h, y+h*s1);
s3 = feval(FunFcn, t+h/2, y+h*(s1+s2)/4);
% Estimate the error and the acceptable error
delta = norm(h*(s1 - 2*s3 + s2)/3,'inf');
tau = tol*max(norm(y,'inf'),1.0);
% Update the solution only if the error is acceptable
ts = t;
ys = y;
if delta <= tau
t = t + h;
y = y + h*(s1 + 4*s3 + s2)/6;
% Update the plot
Y = [y Y(:,1:L-1)];
set(head,'xdata',Y(1,1),'ydata',Y(2,1),'zdata',Y(3,1))
set(body,'xdata',Y(1,1:2),'ydata',Y(2,1:2),'zdata',Y(3,1:2))
set(tail,'xdata',Y(1,L-1:L),'ydata',Y(2,L-1:L),'zdata',Y(3,L-1:L))
drawnow;
end
% Update the step size
if delta ~= 0.0
h = min(hmax, 0.9*h*(tau/delta)^pow);
end
end; % Main loop ...
% ====== End of Demo
set([startHndl closeHndl infoHndl],'Enable','on');
set(stopHndl,'Enable','off');
elseif strcmp(action,'info');
helpwin(mfilename);
end; % if strcmp(action, ...
function ydot = lorenzeq(t,y)
% GLCF中，只有一个实标量参数τ，确定系统的混沌行为，而特征值满足一个
% (且只有一个)非常简单的不等式条件：
% -L2 > L1 > -L3 > 0
L1 = 2;
L2 = -3;
L3 = -1;
T = 1;
A = diag([L1 L2 L3]);
c = [1 -1 0];
B = [0 0 -1; 0 0 -1; 1 T 0];
ydot = A*y + c*y * b * y;
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