資源簡介
計算混沌系統的李雅普諾夫指數,穩定體系的相軌線相應于趨向某個平衡點,如果出現越來越遠離平衡點,則系統是不穩定的。系統只要有一個正值就會出現混沌運動。
判斷一個非線性系統是否存在混沌運動時,需要檢查它的李雅普諾夫指數λ是否為正值。
在高維相空間中大于零的李雅普諾夫指數可能不止一個,這樣體系的運動將更為復雜。人們稱高維相空間中有多個正值指數的混沌為超混沌。推廣到高維空間后,有指數(λ1,λ2,λ3,···)的值決定的各種類型的吸引子可以歸納為

代碼片段和文件信息
function?[DATAAxisRange]=demoparm(system)
%DEMOPARM????Parameters?for?demo?systems
%????????????The?demo?systems?include:
%?????????????1)?Logistic?map
%?????????????2)?Henon?map
%?????????????3)?Duffing‘s?equation
%?????????????4)?Lorenz?equation
%?????????????5)?Rossler?equation
%?????????????6)?Van?Der?Pol?equation
%?????????????7)?Stewart-McCumber?model
%????????????by?Steve?W.?K.?SIU?July?5?1998.
%-------Common?parameters--------
output=0;???????????????????%Don‘t?check?“Output?File“:?1=“check“?0=“uncheck“
LEout=0;????????????????????%Don‘t?check?“Lyapunov?Exponents“
ODEout=0;???????????????????%Don‘t?check?“Lyapunov?Dimension“
LEprecision=1;??????????????%Precision?of?output?values?of?the
ODEprecision=1;?????????????%???????Lyapunov?exponents?and?dimension
????????????????????????????%???????1=“%.4f“?2=“%.6f‘?...?5=“.12f“
%Line?Colors
Blue=1;?Black=2;?Green=3;?Red=4;?Yellow=5;?Magenta=6;?Cyan=7;
LineColor=Blue;??????????????%??line?color:?Blue
switch?system
case?‘Logistic?map‘
???%Parameters?for?logistic?map
???IntMethod=1;?????????????%Integration?method:?1=Discrete?map?2=ODE45?3=ODE23
????????????????????????????%?4=ODE113?5=ODE23S?6=ODE15S
???InitialTime=0;???????????%Initial?time:?0
???FinalTime=30000;?????????%Total?time?steps:?30000
???TimeStep=1;??????????????%Time?step:?1
???RelTol=0;????????????????%Relative?tolerance:?N.A.
???AbsTol=0;????????????????%Absolute?tolerance:?N.A.
???IC=[0.1];????????????????%Initial?conidition
???LODEnum=1;???????????????%No.?of?linearized?ODEs
???%PLOTTING?OPTIONS:???Only?one?of?them?can?be?set?“on“?(i.e.?1)
???plot1=0;?????????????????%Plot?immediately
???plot2=1;?????????????????%Plot?every??ItrNum?iterations
???ItrNum=20;
???Discard=200;?????????%Transient?iterations?to?be?discarded:?200?iterations?=?200*10?time?steps
???UpdateSteps=10;??????%Update?the?LEs?every?10?time?steps
???%Axis?range?for?plotting
???AxisRange=[InitialTimeFinalTime0.50.8];
case?‘Henon?map‘
???%Parameters?for?Henon?map
???IntMethod=1;??????????%Integration?method:?1=Discrete?map?2=ODE45?3=ODE23
?????????????????????????%?4=ODE113?5=ODE23S?6=ODE15S
???InitialTime=0;????????%Initial?time:?0
???FinalTime=20000;??????%Total?time?steps:?20000
???TimeStep=1;???????????%Time?step:?1
???RelTol=0;?????????????%Relative?tolerance:?N.A.
???AbsTol=0;?????????????%Absolute?tolerance:?N.A.
???IC=[0?0];?????????????%Initial?coniditions
???LODEnum=4;????????????%No.?of?linearized?ODEs
???%PLOTTING?OPTIONS:???Only?one?of?them?can?be?set?“on“?(i.e.?1)
???plot1=0;??????????????%Plot?immediately
???plot2=1;??????????????%Plot?every??ItrNum?iterations
???ItrNum=20;
???Discard=500;??????????%Transient?iterations?to?be?discarded:?500
???UpdateSteps=1;????????%Update?the?LEs?every?time?step
?????????????????????????%?UpdateSteps?>?0?will?cause?overflow
???%Axis?range?for?plotting
???AxisRange=[InitialTimeFinalTime-21];
case?‘Duffing‘‘s?equa
?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件???????1453??2010-04-06?19:49??lorenzeq.m
?????文件??????11589??2010-04-06?19:49??readme.m
?????文件???????1238??2010-04-06?19:50??rossler.m
?????文件???????5653??2010-04-06?19:51??sethelp.m
?????文件??????31576??2010-04-06?19:52??setting.m
?????文件???????5700??2010-04-06?19:52??startlet.m
?????文件???????1313??2010-04-06?19:53??stewart.m
?????文件???????1205??2010-04-06?19:53??vderpol.m
?????文件???????8431??2010-04-06?19:46??demoparm.m
?????文件???????1974??2010-06-02?16:35??duffing.m
?????文件??????11276??2010-04-06?19:47??findlyap.m
?????文件??????20704??2010-04-06?19:47??let.m
?????文件?????101030??2010-04-06?19:44??LET.txt
?????文件???????2302??2010-04-06?19:47??lethelp.m
?????文件????????681??2010-04-06?19:48??logistic.m
-----------?---------??----------?-----??----
???????????????206125????????????????????15
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