%%响应系统参数跟驱动系统一样
function MMAMNNs
t0 = 0;
tfinal =50;
tspan = t0:0.01:tfinal; %设置步长
sol = ddesd(@differentical,@delay,@hist,tspan);
tint = linspace(0,tfinal,1500);
yint = deval(sol,tint);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure;
plot3(yint(1,:),yint(2,:),yint(3,:),'-b',yint(4,:),yint(5,:),yint(6,:),'-r');
xlabel('x_{11}(t) or y_{11}(t)')
ylabel('x_{21}(t) or y_{21}(t)')
zlabel('x_{31}(t) or y_{31}(t)')
legend('x','y');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure;
plot(tint,yint(1,:),' - r',tint,yint(4,:),' -c',tint,yint(2,:),' - b',tint,yint(5,:),' -m',tint,yint(3,:),'-g',tint,yint(6,:),'-k', 'LineWidth',1);%第一个节点的x状态和y状态
xlabel('Time-t')
ylabel('Amplitude')
legend('x_{11}(t)','y_{11}(t)','x_{21}(t)','y_{21}(t)','x_{31}(t)','y_{31}(t)')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure;
plot(tint,yint(4,:)-yint(1,:),'b-',tint,yint(5,:)-yint(2,:),'r-',tint,yint(6,:)-yint(3,:),'k-');
xlabel('t');
ylabel('e_{11}(t)e_{21}(t)e_{31}(t)');
legend('e_{11}(t)','e_{21}(t)','e_{31}(t)');
max(abs(yint(4,:)-yint(1,:)))
min(abs(yint(4,:)-yint(1,:)))
%% 误差
figure
subplot(3,1,1)
plot(tint,yint(4,:)-yint(1,:),'r', 'LineWidth',1);
xlabel('Time-t')
ylabel('e_{11}(t)')
subplot(3,1,2)
plot(tint,yint(5,:)-yint(2,:),' - c', 'LineWidth',1);
xlabel('Time-t')
ylabel('e_{21}(t)')
subplot(3,1,3)
plot(tint,yint(6,:)-yint(3,:),'-g', 'LineWidth',1);
xlabel('Time-t')
ylabel('e_{31}(t)')
end
%分布时滞的原函数
%syms t s
%distributed = int(tanh(s),t-0.5*sin(t)-0.5,t)
%原函数为:log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2))
% log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2))
%时变时延
function d=delay(t,y)
d = [t-0.5*cos(t)-0.5;t-0.001;t-0.5*cos(t)-0.5-0.001; t-0.5*sin(t)-0.5]
end
%初始值
function h=hist(t)
% h=[ 2.8;1.85;1.37;2.5;1.97;0.75];%误差
h=[2;1.2;-1;2.5;1.97;0.75];
% h=[0.02;-0.06;-0.02;0.8; -0.2; -0.1];%混沌
end
%x无控制器,y有控制器,第1,2,3是驱动系统,第4,5,6是响应系统
function dydt = differentical(t,y,Z)
a=0;
b=0;
c=0;
% s1=sign(y(4)-y(1));
% s2=sign(y(5)-y(2));
% s3=sign(y(6)-y(3));
s1=(y(4)-y(1))/(abs(y(4)-y(1))+0.01);
s2=(y(5)-y(2))/(abs(y(5)-y(2))+0.01);
s3=(y(6)-y(3))/(abs(y(6)-y(3))+0.01);
% D=[0.87; 0.34; 0.55];%混沌
% A=[0.1,0.21; 0.2,0.53; -0.37,0.21; -0.92,0.2; 0.45,0.86; 0.58,0.79;];
% B=[-0.25,0.04; -0.15,-0.1; 0.03,0.04; -0.19,-0.22; 0.52,-0.01; 0.54,0.67;];
% C=[-0.11,-0.01; 0.02,-0.3; 0.05,-0.14; 0.05,-0.01; 0.4,-0.13; 0.08,0.1;];
D=[0.25 0.56 1.56]+0.1; %误差
A=[0.36,0.89; 0.85,-0.48; 0.99,-0.18; 0.88,0.53; 1,0.2; -0.28,-0.55; ]-0.3;
B=[1.03,0.31; 0.21,0.58; 0.24,0.15; 0.25,0.34; -0.4,0.21; 0.3,0.31; ]+0.4;
C=[0.78,-0.28; 1.4,0.85; -0.2,0.53; 0.1,0.2; 0.25,0.18; 0.23,0.5; ]*-0.4+0.1;
M=sin(t)/2 - t + 1/2;
h3=1;h4=1;
p=0.7;q=3;
d=0.001;
dy=(y-Z(:,2))/d;
dy_delay=(-Z(:,3)+Z(:,1))'/d;
dAC=[dy(2)*f_d(y(2))-dy(1);dy(3)*f_d(y(3))-dy(1); dy(1)*f_d(y(1))-dy(2);dy(3)*f_d(y(3))-dy(2); dy(1)*f_d(y(1))-dy(3);dy(2)*f_d(y(2))-dy(3);];
dyAC=[dy(5)*f_d(y(5))-dy(4);dy(6)*f_d(y(6))-dy(4); dy(4)*f_d(y(4))-dy(5);dy(6)*f_d(y(6))-dy(5); dy(4)*f_d(y(4))-dy(6);dy(5)*f_d(y(5))-dy(6);];
dB=[dy_delay(2)*f_d(Z(2,1))-dy(1);dy_delay(3)*f_d(Z(3,1))-dy(1); dy_delay(1)*f_d(Z(1,1))-dy(2);dy_delay(3)*f_d(Z(3,1))-dy(2); dy_delay(1)*f_d(Z(1,1))-dy(3);dy_delay(2)*f_d(Z(2,1))-dy(3);];
dyB=[dy_delay(5)*f_d(Z(5,1))-dy(4);dy_delay(6)*f_d(Z(6,1))-dy(4); dy_delay(4)*f_d(Z(4,1))-dy(5);dy_delay(6)*f_d(Z(6,1))-dy(5); dy_delay(4)*f_d(Z(4,1))-dy(6);dy_delay(5)*f_d(Z(5,1))-dy(6);];
u1=-0.8*(y(4)-y(1))+s1*(-abs(y(5)-y(2))-abs(y(6)-y(3))-0.7*abs(Z(5)-Z(2))-0.7*abs(Z(6)-Z(3))-0.5*(0.5*sin(t)-0.5)*abs(y(5)-y(2))-0.5*(0.5*sin(t)-0.5)*abs(y(6)-y(3)))+s1*( -2*abs(y(2))-2*abs(y(3))-0.9*(abs(Z(2))+abs(Z(3)))-0.55*(0.5*sin(t)-0.5)*(abs(y(2))+abs(y(3))))-1.2*s1*abs(y(4)-y(1))^0.5-1.2*s1*abs(y(4)-y(1))^4;
u2=-(y(5)-y(2))+s2*(-1.5*abs(y(4)-y(1))-1.5*abs(y(6)-y(3))-0.9*abs(Z(4)-Z(1))-0.9*abs(Z(6)-Z(3))-0.6*(0.5*sin(t)-0.5)*abs(y(4)-y(1))-0.6*(0.5*sin(t)-0.5)*abs(y(6)-y(3))) +s2*( -0.8*abs(y(1))-0.8*abs(y(3))-1.2*(abs(Z(1))+abs(Z(3)))-0.6*(0.5*sin(t)-0.5)*(abs(y(1))+abs(y(3))))-1.2*s2*abs(y(5)-y(2))^0.5-1.2*s2*abs(y(5)-y(2))^4;
u3=0.5*(y(6)-y(3))+s3*(-abs(y(4)-y(1))-abs(y(5)-y(2))-1.5*abs(Z(4)-Z(1))-1.5*abs(Z(5)-Z(2))-(0.5*sin(t)-0.5)*abs(y(4)-y(1))-(0.5*sin(t)-0.5)*abs(y(5)-y(2))) +s3*( -1.7*abs(y(1))-1.7*abs(y(2))-0.4*(abs(Z(1))+abs(Z(2)))-0.3*(0.5*sin(t)-0.5)*(abs(y(1))+abs(y(2))))-1.2*s3*abs(y(6)-y(3))^0.5-1.2*s3*abs(y(6)-y(3))^4;
u=[u1;u2;u3];
% y(1:3)-y(4:6)
dydt =[
% -D(1,1)*y(1)*(abs(y(1))<=a)-D(1,2)*y(1)*(abs(y(1))>a)+A(3,1)*tanh(y(2))*(abs(y(1))<=a)+A(3,2)*tanh(y(2))*(abs(y(1))>a)+A(5,1)*tanh(y(3))*(abs(y(1))<=a)+A(5,2)*tanh(y(3))*(abs(y(1))>a)+B(3,1)*tanh(Z(2,1))*(abs(y(1))<=a)+B(3,2)*tanh(Z(2,1))*(abs(y(1))>a)+B(5,1)*tanh(Z(3,1))*(abs(y(1))<=a)+B(5,2)*tanh(Z(3,1))*(abs(y(1))>a)+C(3,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(1))<=a)+C(3,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(1))>a)+C(5,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(1))<=a)+C(5,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(1))>a);
% -D(2,1)*y(2)*(abs(y(2))<=b)-D(2,2)*y(2)*(abs(y(2))>b)+A(1,1)*tanh(y(1))*(abs(y(2))<=b)+A(1,2)*tanh(y(1))*(abs(y(2))>b)+A(6,1)*tanh(y(3))*(abs(y(2))<=b)+A(6,2)*tanh(y(3))*(abs(y(2))>b)+B(1,1)*tanh(Z(1,1))*(abs(y(2))<=b)+B(1,2)*tanh(Z(1,1))*(abs(y(2))>b)+B(6,1)*tanh(Z(3,1))*(abs(y(2))<=b)+B(6,2)*tanh(Z(3,1))*(abs(y(2))>b)+C(1,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(2))<=b)+C(1,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(2))>b)+C(6,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(2))<=b)+C(6,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(2))>b);
% -D(3,1)*y(3)*(abs(y(3))<=c)-D(3,2)*y(3)*(abs(y(3))>c)+A(2,1)*tanh(y(1))*(abs(y(3))<=c)+A(2,2)*tanh(y(1))*(abs(y(3))>c)+A(4,1)*tanh(y(2))*(abs(y(3))<=c)+A(4,2)*tanh(y(2))*(abs(y(3))>c)+B(2,1)*tanh(Z(1,1))*(abs(y(3))<=c)+B(2,2)*tanh(Z(1,1))*(abs(y(3))>c)+B(4,1)*tanh(Z(2,1))*(abs(y(3))<=c)+B(4,2)*tanh(Z(2,1))*(abs(y(3))>c)+C(2,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(3))<=c)+C(2,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(3))>c)+C(4,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(3))<=c)+C(4,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(3))>c);
%
% -D(1,1)*y(4)*(abs(y(4))<=a)-D(1,2)*y(4)*(abs(y(4))>a)+A(3,1)*tanh(y(5))*(abs(y(4))<=a)+A(3,2)*tanh(y(5))*(abs(y(4))>a)+A(5,1)*tanh(y(6))*(abs(y(4))<=a)+A(5,2)*tanh(y(6))*(abs(y(4))>a)+B(3,1)*tanh(Z(5,1))*(abs(y(4))<=a)+B(3,2)*tanh(Z(5,1))*(abs(y(4))>a)+B(5,1)*tanh(Z(6,1))*(abs(y(4))<=a)+B(5,2)*tanh(Z(6,1))*(abs(y(4))>a)+C(3,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(4))<=a)+C(3,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(4))>a)+C(5,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(4))<=a)+C(5,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(4))>a)-0.7*(y(4)-y(1))-9.12*s1-h3*s1*(abs(y(4)-y(1)))^p-h4*s1*(y(4)-y(1))^q;
% -D(2,1)*y(5)*(abs(y(5))<=b)-D(2,2)*y(5)*(abs(y(5))>b)+A(1,1)*tanh(y(4))*(abs(y(5))<=b)+A(1,2)*tanh(y(4))*(abs(y(5))>b)+A(6,1)*tanh(y(6))*(abs(y(5))<=b)+A(6,2)*tanh(y(6))*(abs(y(5))>b)+B(1,1)*tanh(Z(4,1))*(abs(y(5))<=b)+B(1,2)*tanh(Z(4,1))*(abs(y(5))>b)+B(6,1)*tanh(Z(6,1))*(abs(y(5))<=b)+B(6,2)*tanh(Z(6,1))*(abs(y(5))>b)+C(1,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(5))<=b)+C(1,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(5))>b)+C(6,1)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(5))<=b)+C(6,2)*(log(cosh(t)) - log(cosh(sin(t)/2 - t + 1/2)))*(abs(y(5))>b)-0.9*(y(5)-y(2))-12.93*s2-h3*s2*(abs(y(5)-y(2)))^p-h4*s2*(y(5)-y(2))^q;
% -D(3,1)*y(6)*(abs(y(6))<=c)-D(3,2)*y(6)*(