function?[xyz]=lorentz（nlevelsrbx0y0z0h）
%Syntax:?[xyz]=lorentz（nlevelsrbx0y0z0h）
%_________________________________________________
%
%?Simulation?of?the?Lorentz?ODE.
%????dx/dt=s*（y-x）
%????dy/dt=r*x-y-xz
%????dz/dt=x*y-b*z;
%
%?x?y?and?z?are?the?simulated?time?series.
%?n?is?the?number?of?the?simulated?points.
%?level?is?the?noise?standard?deviation?divided?by?the?standard?deviation?of?the
%???noise-free?time?series.?We?assume?Gaussian?noise?with?zero?mean.
%?s?r?b?and?s?are?the?parameters
%?x0?is?the?initial?value?for?x.
%?y0?is?the?initial?value?for?y.
%?z0?is?the?initial?value?for?z.
%?h?is?the?step?size.
%
%
%?Notes:
%?The?time?is?n*h.
%?The?integration?is?obtained?by?the?Euler‘s?method.
%
%
%?Reference:
%
%?Lorentz?E?N?（1963）:?Deterministic?nonperiodic?flow.?Journal?of?the
%?Atmosphairic?Sciences?20:?130-141
%
%
%?Alexandros?Leontitsis
%?Department?of?Education
%?University?of?Ioannina
%?45110?-?Dourouti
%?Ioannina
%?Greece
%?
%?University?e-mail:?me00743@cc.uoi.gr
%?Lifetime?e-mail:?leoaleq@yahoo.com
%?Homepage:?http://www.geocities.com/CapeCanaveral/Lab/1421
%
%?16?Nov?2001

if?nargin<1?|?isempty（n）==1
????n=500;
else
????%?n?must?be?scalar
????if?sum（size（n））>2
????????error（‘n?must?be?scalar.‘）;
????end
????%?n?must?be?positive
????if?n<0
????????error（‘n?must?be?positive.‘）;
????end
????%?n?must?be?an?integer
????if?round（n）-n~=0
????????error（‘n?must?be?an?integer.‘）;
????end
end

if?nargin<2?|?isempty（level）==1
????level=0;
else
????%?level?must?be?scalar
????if?sum（size（level））>2
????????error（‘level?must?be?scalar.‘）;
????end
????%?level?must?be?positive
????if?level<0
????????error（‘level?must?be?positive.‘）;
????end
end

if?nargin<3?|?isempty（s）==1
????s=16;
else
????%?s?must?be?scalar
????if?sum（size（s））>2
????????error（‘s?must?be?scalar.‘）;
????end
end

if?nargin<4?|?isempty（r）==1
????r=45.92;
else
????%?r?must?be?scalar
????if?sum（size（r））>2
????????error（‘r?must?be?scalar.‘）;
????end
end

if?nargin<5?|?isempty（b）==1
????b=4;
else
????%?b?must?be?scalar
????if?sum（size（b））>2
????????error（‘b?must?be?scalar.‘）;
????end
end

if?nargin<6?|?isempty（x0）==1
????x0=0.1;
else
????%?x0?must?be?scalar
????if?sum（size（x0））>2
????????error（‘x0?must?be?scalar.‘）;
????end
end

if?nargin<7?|?isempty（y0）==1
????y0=0.1;
else
????%?y0?must?be?scalar
????if?max（size（y0））>2
????????error（‘y0?must?be?scalar.‘）;
????end
end

if?nargin<8?|?isempty（z0）==1
????z0=0.1;
else
????%?z0?must?be?scalar
????if?max（size（z0））>2
????????error（‘z0?must?be?scalar.‘）;
????end
end

if?nargin<9?|?isempty（h）==1
???h=0.01;
else
????%?h?must?be?scalar
????if?max（size（h））>2
????????error（‘h?must?be?scalar.‘）;
????end
????%?h?must?be?positive
????if?h<0
????????error（‘h?must?be?positive.‘）;
????end
end

%?Initialize
y（1:）=[x0?y0?z0];

%?Simulate
for?i=2:n
????ydot（1）=s*（y（i-12）-y（i-11））;
????ydot（

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????3299??2003-10-29?21:30??encryption\lorentz.m

?????文件???????2286??2006-07-02?10:55??encryption\算法.m

?????目錄??????????0??2008-01-04?18:46??encryption

-----------?---------??----------?-----??----

?????????????????5803????????????????????4