function[T,E]=TCSMC3(parameters,orders,TSim,E0)
h=0.001;
n=round(TSim/h);
q1=orders(1);q2=orders(2);q3=orders(3);q4=orders(4);
k=parameters(1);a=parameters(2);mu=parameters(3);p=parameters(4);
cp1=1;cp2=1;cp3=1;cp4=1;cp5=1;cp6=1;cp7=1;cp8=1;cp9=1;cp10=1;
for j=1:n
c1(j)=(1-(1+q1)/j)*cp1;
c2(j)=(1-(1+q2)/j)*cp2;
c3(j)=(1-(1+q3)/j)*cp3;
c4(j)=(1-(1-2*q1)/j)*cp4;
c5(j)=(1-(1+(q1-1))/j)*cp5;
c6(j)=(1-(1+(q1-2))/j)*cp6;
c7(j)=(1-(1-1)/j)*cp7;
c8(j)=(1-(1-q1)/j)*cp8;
c9(j)=(1-(2-q1)/j)*cp9;
c10(j)=(1-(1+2*q1)/j)*cp10;
cp1=c1(j);cp2=c2(j);cp3=c3(j);cp4=c4(j);cp5=c5(j);cp6=c6(j);
cp7=c7(j);cp8=c8(j);cp9=c9(j);cp10=c10(j);
end
s11(1)=E0(1);s12(1)=E0(2);s13(1)=E0(3);s14(1)=E0(4);
s21(1)=E0(5);s22(1)=E0(6);s23(1)=E0(7);s24(1)=E0(8);
x1(1)=E0(9);x2(1)=E0(10);x3(1)=E0(11);x4(1)=E0(12);
y1(1)=E0(13);y2(1)=E0(14);y3(1)=E0(15);y4(1)=E0(16);
u11(1)=E0(17);u12(1)=E0(18);u13(1)=E0(19);u14(1)=E0(20);
u21(1)=E0(21);u22(1)=E0(22);u23(1)=E0(23);u24(1)=E0(24);
theta1(1)=E0(25);theta2(1)=E0(26);theta3(1)=E0(27);theta4(1)=E0(28);
theta5(1)=E0(29);theta6(1)=E0(30);theta7(1)=E0(31);theta8(1)=E0(32);
for i=2:n
e1(i) = y1(i-1) - x1(i-1);
e2(i) = y2(i-1) - x2(i-1);
e3(i) = y3(i-1) - x3(i-1);
e4(i) = y4(i-1) - x4(i-1);
D_rho1_e1(i) = (1/gamma(1 - (q1))) * h^(-(q1)) * (e1(i)+memo(e1, c1, i-1));
D_rho1_e2(i) = (1/gamma(1 - (q2))) * h^(-(q2)) * (e2(i)+memo(e2, c1, i-1));
D_rho1_e3(i) = (1/gamma(1 - (q3))) * h^(-(q3)) * (e3(i)+memo(e3, c1, i-1));
D_rho1_e4(i) = (1/gamma(1 - (q4))) * h^(-(q4)) * (e4(i)+memo(e4, c1, i-1));
term1(i) = e1(i)+sign(e1(i))*abs(e1(i))^(1-a);
term2(i) = e2(i)+sign(e2(i))*abs(e2(i))^(1-a);
term3(i) = e3(i)+sign(e3(i))*abs(e3(i))^(1-a);
term4(i) = e4(i)+sign(e4(i))*abs(e4(i))^(1-a);
D_rho1_term1(i) = (1/gamma(1 - (-q1))) * h^(-(-q1)) * (term1(i)+memo(term1, c8, i-1));
D_rho1_term2(i) = (1/gamma(1 - (-q2))) * h^(-(-q2)) * (term2(i)+memo(term2, c8, i-1));
D_rho1_term3(i) = (1/gamma(1 - (-q3))) * h^(-(-q3)) * (term3(i)+memo(term3, c8, i-1));
D_rho1_term4(i) = (1/gamma(1 - (-q4))) * h^(-(-q4)) * (term4(i)+memo(term4, c8, i-1));
s11(i)=D_rho1_e1(i)+2*k*e1(i)+k*sign(e1(i))*abs(e1(i))^(1-a)+(k^2)*D_rho1_term1(i);
s12(i)=D_rho1_e2(i)+2*k*e2(i)+k*sign(e2(i))*abs(e2(i))^(1-a)+(k^2)*D_rho1_term2(i);
s13(i)=D_rho1_e3(i)+2*k*e3(i)+k*sign(e3(i))*abs(e3(i))^(1-a)+(k^2)*D_rho1_term3(i);
s14(i)=D_rho1_e4(i)+2*k*e4(i)+k*sign(e4(i))*abs(e4(i))^(1-a)+(k^2)*D_rho1_term4(i);
s21(i)=D_rho1_e1(i)+k*sign(e1(i))*abs(e1(i))^(1-a)-(k^2)*D_rho1_term1(i);
s22(i)=D_rho1_e2(i)+k*sign(e2(i))*abs(e2(i))^(1-a)-(k^2)*D_rho1_term2(i);
s23(i)=D_rho1_e3(i)+k*sign(e3(i))*abs(e3(i))^(1-a)-(k^2)*D_rho1_term3(i);
s24(i)=D_rho1_e4(i)+k*sign(e4(i))*abs(e4(i))^(1-a)-(k^2)*D_rho1_term4(i);
s1(i)=s11(i)+s21(i);
s2(i)=s12(i)+s22(i);
s3(i)=s13(i)+s23(i);
s4(i)=s14(i)+s24(i);
D_rho1_s11(i) = (1/gamma(1 - (-q1))) * h^(-(-q1)) * (s11(i)+memo(s11, c8, i-1));
D_rho1_s12(i) = (1/gamma(1 - (-q2))) * h^(-(-q2)) * (s12(i)+memo(s12, c8, i-1));
D_rho1_s13(i) = (1/gamma(1 - (-q3))) * h^(-(-q3)) * (s13(i)+memo(s13, c8, i-1));
D_rho1_s14(i) = (1/gamma(1 - (-q4))) * h^(-(-q4)) * (s14(i)+memo(s14, c8, i-1));
u11(i)=(-20*x1(i-1)+35*x2(i-1)-x4(i-1))...
-(y2(i-1))...
-2*k*e1(i)-k*sign(e1(i))*abs(e1(i))^(1-a)-(k^2)*D_rho1_term1(i);
u12(i)=(30*x1(i-1)-x1(i-1)*x3(i-1)-x2(i-1))...
-(-y1(i-1)+y2(i-1)*y3(i-1))...
-2*k*e2(i)-k*sign(e2(i))*abs(e2(i))^(1-a)-(k^2)*D_rho1_term2(i);
u13(i)=(x1(i-1)*x2(i-1)-5*(x1(i-1)+x3(i-1)))...
-(-y1(i-1)-10*y1(i-1)*y2(i-1)-y1(i-1)*y3(i-1))...
-2*k*e3(i)-k*sign(e3(i))*abs(e3(i))^(1-a)-(k^2)*D_rho1_term3(i);
u14(i)=(16*(x1(i-1)+x2(i-1)))...
-(-y1(i-1)*y2(i-1)+y4(i-1))...
-2*k*e4(i)-k*sign(e4(i))*abs(e4(i))^(1-a)-(k^2)*D_rho1_term4(i);
zerm1(i) = sign(s1(i));
zerm2(i) = sign(s2(i));
zerm3(i) = sign(s3(i));
zerm4(i) = sign(s4(i));
D_rho1_zerm1(i) = (1/gamma(1 - (-q1))) * h^(-(-q1)) * (zerm1(i)+memo(zerm1, c8, i-1));
D_rho1_zerm2(i) = (1/gamma(1 - (-q2))) * h^(-(-q2)) * (zerm2(i)+memo(zerm2, c8, i-1));
D_rho1_zerm3(i) = (1/gamma(1 - (-q3))) * h^(-(-q3)) * (zerm3(i)+memo(zerm3, c8, i-1));
D_rho1_zerm4(i) = (1/gamma(1 - (-q4))) * h^(-(-q4)) * (zerm4(i)+memo(zerm4, c8, i-1));
u21(i)=-(theta1(i-1))*D_rho1_zerm1(i);
u22(i)=-(theta2(i-1))*D_rho1_zerm2(i);
u23(i)=-(theta3(i-1))*D_rho1_zerm3(i);
u24(i)=-(theta4(i-1))*D_rho1_zerm4(i);
u1(i)=u11(i)+u21(i);
u2(i)=u12(i)+u22(i);
u3(i)=u13(i)+u23(i);
u4(i)=u14(i)+u24(i);
x1(i)=(-20*x1(i-1)+35*x2(i-1)-x4(i-1)-0.25*x1(i-1)*sin(4*(i-1))+0.1*cos((i-1)))*h^q1-memo(x1,c1,i);
x2(i)=(30*x1(i-1)-x1(i-1)*x3(i-1)-x2(i-1)-0.25*cos(2*(i-1))*x2(i-1)+0.1*cos((i-1)))*h^q1-memo(x2,c1,i);
x3(i)=(x1(i-1)*x2(i-1)-5*(x1(i-1)+x3(i-1))+0.1*sin(3*(i-1))*x3(i-1)+0.1*cos(2*(i-1)))*h^q1-memo(x3,c1,i);
x4(i)=(16*(x1(i-1)+x2(i-1))-0.25*cos(2*(i-1))*x4(i-1)+0.1*sin((i-1)))*h^q1-memo(x4,c1,i);
y1(i)=(y2(i-1)-0.15*sin(4*(i-1))*y1(i-1)+0.1*sin((i-1))+u1(i))*h^q2-memo(y1,c2,i);
y2(i)=(-y1(i-1)+y2(i-1)*y3(i-1)+0.15*cos(4*(i-1))*y2(i-1)+0.1*sin((i-1))+u2(i))*h^q2-memo(y2,c2,i);
y3(i)=(-y1(i-1)-10*y1(i-1)*y2(i-1)-y1(i-1)*y3(i-1)+0.15*sin(4*(i-1))*y3(i-1)+0.1*sin((i-1))+u3(i))*h^q2-memo(y3,c2,i);
y4(i)=(-y1(i-1)*y2(i-1)+y4(i-1)-0.25*sin(i-1)*y4(i-1)+0.1*sin((i-1))+u4(i))*h^q2-memo(y4,c2,i);
abs_s1(i)=abs(s1(i));
abs_s2(i)=abs(s2(i));
abs_s3(i)=abs(s3(i));
abs_s4(i)=abs(s4(i));
D_rho1_abs_s1(i) = (1/gamma(1 - (-q1))) * h^(-(-q1)) * (abs_s1(i)+memo(abs_s1, c8, i-1));
D_rho1_abs_s2(i) = (1/gamma(1 - (-q2))) * h^(-(-q2)) * (abs_s2(i)+memo(abs_s2, c8, i-1));
D_rho1_abs_s3(i) = (1/gamma(1 - (-q3))) * h^(-(-q3)) * (abs_s3(i)+memo(abs_s3, c8, i-1));
D_rho1_abs_s4(i) = (1/gamma(1 - (-q4))) * h^(-(-q4)) * (abs_s4(i)+memo(abs_s4, c8, i-1));
theta1(i)=mu*D_rho1_abs_s1(i);
theta2(i)=mu*D_rho1_abs_s2(i);
theta3(i)=mu*D_rho1_abs_s3(i);
theta4(i)=mu*D_rho1_abs_s4(i);
theta5(i)=mu*D_rho1_abs_s1(i);
theta6(i)=mu*D_rho1_abs_s2(i);
theta7(i)=mu*D_rho1_abs_s3(i);
theta8(i)=mu*D_rho1_abs_s4(i);
end
for j=1:n
E(j,1)=s11(j);
E(j,2)=s12(j);
E(j,3)=s13(j);
E(j,4)=s14(j);
E(j,5)=s21(j);
E(j,6)=s22(j);
E(j,7)=s23(j);
E(j,8)=s24(j);
E(j,9)=x1(j);
E(j,10)=x2(j);
E(j,11)=x3(j);
E(j,12)=x4(j);
E(j,13)=y1(j);
E(j,14)=y2(j);
E(j,15)=y3(j);
E(j,16)=y4(j);
E(j,17)=u11(j);
E(j,18)=u12(j);
E(j,19)=u13(j);
E(j,20)=u14(j);
E(j,21)=u21(j);
E(j,22)=u22(j);
E(j,23)=u23(j);
E(j,24)=u24(j);
E(j,25)=theta1(j);
E(j,26)=theta2(j);
E(j,27)=theta3(j);
E(j,28)=theta4(j);
E(j,29)=theta5(j);
E(j,30)=theta6(j);
E(j,31)=theta7(j);
E(j,32)=theta8(j);
end
T=h:h:TSim;
end
[t,y]=TCSMC3([5.5 0.35 0.08 0.05],...
[0.987 0.987 0.987 0.987]...
,2,[1 1 1 1 ...
1 1 1 1 ...
-3.2 -8.5 3.5 3.3...
0.3 0.5 0.5 0.2 ...
0.1 0.1 0.1 0.1 ...
0.1 0.1 0.1 0.1 ...
0 0 0 0 ...
0 0 0 0 ...
]);
figure(1);
subplot(4,1,1);
plot(t,y(:,9),'b-',t,y(:,13),'r--');
xlabel('Time(sec)');
ylabel('{x}_{1},{y}_{1}')
title('a')
grid on;
subplot(4,1,2);
plot(t,y(:,10),'b-',t,y(:,14),'r--');
xlabel('Time(sec)');
ylabel('{x}_{2},{y}_{2}')
title('b')
grid on;
subplot(4,1,3);
plot(t,y(:,11),'b-',t,y(:,15),'r--');
xlabel('Time(sec)');
ylabel('{x}_{3},{y}_{3}')
title('c')
grid on;
subplot(4,1,4);
plot(t,y(:,12),'b-',t,y(:,16),'r--');
xlabel('Time(sec)');
ylabel('{x}_{4},{y}_{4}')
title('d')
grid on;
figure(2);
subplot(4,1,1);
plot(t,y(:,13)-y(:,9),'k');
xlabel('Time(sec)');
ylabel('{e}_{1}')
title('a')
grid on;
subplot(4,1,2);
plot(t,y(:,14)-y(:,10),'k');
xlabel('Time(sec)');
ylabel('{e}_{2}')
title('b')
grid on;
subplot(4,1,3);
plot(t,y(:,15)-y(:,11),'k');
xlabel('Time(sec)');
ylabel('{e}_{3}')
title('c')
grid on;
subplot(4,1,4);
plot(t,y(:,16)-y(:,12),'k');
xlabel('Time(sec)');
ylabel('{e}_{4}')
title('d')
grid on;
figure(3);
plot(t,y(:,13)-y(:,9),'b-',t,y(:,14)-y(:,10),'r--',t,y(:,15)-y(:,11),'g-',t,y(:,16)-y(:,12),'k-.');
xlabel('Time(sec)');
ylabel('e1,e2,e3,e4')
legend('e1','e2','e3','e4')
title('nice')
grid on;
figure(4);
subplot(2,2,1);
plot(t,y(:,1),'k--')
xlabel('Time(sec)');
ylabel('s11')
title('s11')
grid on;
subplot(2,2,2);
plot(t,y(:,2),'r--')
xlabel('Time(sec)');
ylabel('s12')
title('s12')
grid on;
subplot(2,2,3);
plot(t,y(:,3),'g--')
xlabel('Time(sec)');
ylabel('s13')
title('s13')
grid on;
subplot(2,2,4);
plot(t,y(:,4),'k--')
xlabel('Time(sec)');
ylabel('s14')
title('s14')
grid on;
figure(5);
subplot(2,2,1);
plot(t,y(:,5),'k--')
xlabel('Time(sec)');
ylabel('s21')
title('s21')
grid on;
subplot(2,2,2);
plot(t,y(:,6),'r--')
xlabel('Time(sec)');
ylabel('s22')
title('s22')
grid on;
subplot(2,2,3);
plot(t,y(:,7),'g--')
xlabel('Time(sec)');
ylabel('s23')
title('s23')
grid on;
subplot(2,2,4);
plot(t,y(:,8),'k--')
xlabel('Time(sec)');
ylabel('s24')
title('s24')
grid on;
figure(6);
plot(t,y(:,1)+y(:,5),'b-',t,y(:,2)+y(:,6),'r--',t,y(:,3)+y(:,7),'g-',t,y(:,4)+y(:,8),'k-.');
xlabel('Time(sec)');
ylabel('s1,s2,s3,s4')
legend('s1','s2','s3','s4')
title('nice')
grid on;
figure(7);
plot(t,y(:,1),'b-',t,y(:,5),'k-.',t,y(:,1)+y(:,5),'g-',t,y(:,33),'r--');
xlabel('Time(sec)');
ylabel('s11,')
legend('s11','s21','s1','s5')
title('nice')
grid on;
figure(8);
subplot(2,2,1);
plot(t,y(:,25),'k--')
xlabel('Time(sec)');
ylabel('theta1')
title('theta1')
grid on;
subplot(2,2,2);
plot(t,y(:,26),'r--')
xlabel('Time(sec)');
ylabel('theta2')
title('theta2')
grid on;
subplot(2,2,3);
plot(t,y(:,27),'g--')
xlabel('Time(sec)');
ylabel('theta3')
title('theta3')
grid on;
subplot(2,2,4);
plot(t,y(:,28),'k--')
xlabel('Time(sec)');
ylabel('theta4')
title('theta4')
grid on;
figure(10);
plot3(y(:,9),y(:,10),y(:,11),'g', 'LineWidth', 1.5);
hold on;
plot3(y(:,13),y(:,14),y(:,15), 'r--', 'LineWidth', 1.5);
legend('主系统Chen', '从系统Lorenz');
title('相空间轨迹对比'); xlabel('x_1/y_1'); ylabel('x_2/y_2'); zlabel('x_3/y_3');
grid on;
%} 将前面给你的代码中使用的神经网络方法,应用到我的这个分数阶混沌同步中来,在我的代码基础上进行增加,注意一点要在我的代码基础上改,并将完整的代码输出给我,一定要完整可运行,并将完整的数学模型输出给我,让我可以看懂
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