Maximum Lyapunov exponent with Ode45
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I need to plot Maximum Lyapunov exponent for (x:,5) with variable A ranging (ex: from 1-100). Can you help me? Thank you so much.
function xdot = thefo2l(t,x)
global A
h = 0.002;
b = 160*h;
a = b;
k1 = 0;
k2 = 0;
k3 = 0;
m = 1;
n = 1;
epsilon = 0.1;
q=A*sin(100*t);
A11 =877889. ;
A12 =296675.;
A22 =2.82154*10^7;
A66 =3.02819*10^6 ;
D11 =11.9094 ;
D12 = 4.01856;
D22 =430.583 ;
D66 =1.561;
ro1=2.5954;
%%%%%%%
k11=((-1).*a.^(-2).*A11.*m.^2+(-1).*A66.*b.^(-2).*n.^2).*pi.^2;
k12=(-1).*a.^(-1).*(A12+A66).*b.^(-1).*m.*n.*pi.^2;
k13 = 0;
n1=(-4/9).*((-1)+(-1).^m).*((-1)+(-1).^n).*a.^(-3).*b.^(-2).*n.^(-1).*(2.*( ...
2+(-1).^n).*A11.*b.^2.*m.^2+(-1).*a.^2.*(A12+(-1).*(3+2.*(-1).^n).*A66) ...
.*n.^2).*pi;
k21=(-1).*a.^(-1).*(A12+A66).*b.^(-1).*m.*n.*pi.^2;
k22=((-1).*a.^(-2).*A66.*m.^2+(-1).*A22.*b.^(-2).*n.^2).*pi.^2;
k23=0;
n2=(-4/9).*((-1)+(-1).^m).*((-1)+(-1).^n).*a.^(-2).*b.^(-3).*m.^(-1).*((( ...
-1).*A12+(3+2.*(-1).^m).*A66).*b.^2.*m.^2+2.*(2+(-1).^m).*a.^2.*A22.* ...
n.^2).*pi;
k31 = 0;
k32 = 0;
k33=(-1).*a.^(-4).*b.^(-4).*(b.^4.*D11.*m.^4.*pi.^4+a.^2.*b.^2.*m.^2.* ...
pi.^2.*(b.^2.*k2+2.*(D12+2.*D66).*n.^2.*pi.^2)+a.^4.*(b.^4.*k1+b.^2.* ...
k2.*n.^2.*pi.^2+D22.*n.^4.*pi.^4));
n3=0;
n4=(-1/32).*a.^(-4).*b.^(-4).*(18.*a.^4.*b.^4.*k3+(3.*A11.*b.^4.*m.^4+2.* ...
a.^2.*(3.*A12+(-2).*A66).*b.^2.*m.^2.*n.^2+3.*a.^4.*A22.*n.^4).*pi.^4); ...
n5=(8/9).*((-1)+(-1).^m).*((-1)+(-1).^n).*a.^(-3).*b.^(-2).*n.^(-1).*(2.*( ...
2+(-1).^m).*(2+(-1).^n).*A11.*b.^2.*m.^2+a.^2.*(2.*(2+(-1).^m).*(2+(-1) ...
.^n).*A12+A66).*n.^2).*pi;
n6=(8/9).*((-1)+(-1).^m).*((-1)+(-1).^n).*a.^(-2).*b.^(-3).*m.^(-1).*((2.*( ...
2+(-1).^m).*(2+(-1).^n).*A12+A66).*b.^2.*m.^2+2.*(2+(-1).^m).*(2+(-1) ...
.^n).*a.^2.*A22.*n.^2).*pi;
n7=4.*((-1)+(-1).^m).*((-1)+(-1).^n).*m.^(-1).*n.^(-1).*pi.^(-2).*q;
%%%%%%%%%
xdot = zeros(6,1);
xdot(1) = x(2);
xdot(2) = (k11*x(1)+k12*x(3)+k13*x(5)+n1*x(5)^2)/ro1;
xdot(3) = x(4);
xdot(4) = (k21*x(1)+k22*x(3)+k23*x(5)+n2*x(5)^2)/ro1;
xdot(5) = x(6);
xdot(6) = (k31*x(1)+k32*x(3)+k33*x(5)+n3*x(5)^2+n4*x(5)^3+n5*x(1)*x(3)+n6*x(3)*x(5)+n7)/ro1-2*epsilon*x(6);
xdot = [xdot(1); xdot(2);xdot(3); xdot(4);xdot(5); xdot(6)];
%%%%%%%%%%%%%%%%%%
[t,x] = ode45(@thefo2l,[0 5*2*pi/100],[0 0.0001 0 0.0001 0 0.0001 ]);
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