how to solve the program?

Unrecognized function or variable 'e1'.

s1=x3.^2+x1*x3+x1.^2;
s2=x1.^4+x1.^3*x3+x1.^2*x3.^2 +x1.^2*x3.^2+x1*x3.^3 + x3.^4;
%s1=x2.^2+x1*x2+x1.^2;
%s2=x1.^4+x1.^3*x2+x1.^2*x2.^2 +x1.^2*x2.^3 + x2.^4;

%u1 = -e1-e2;
%u2 = beta*e1*k1 +gamma*e1*k2+omegaf*e1-ff2*cos(W2*t)+ff1*cos(W1*t);
u1 = -e2-e1;
u2 = beta*e1*s1 + gamma*e1*s2+omegaf*e1-ff2*cos(W2*t)+ff1*cos(W1*t);

%sys-I

dx1=x2;
dx2=-alpha*x2-omegaf*x1-beta*x1.^3- gamma*x1.^5+ff1*cos(W1*t);

%sys -II
dx3=x4+u1;
dx4=-alpha*x4-omegaf*x3-beta*x3.^3- gamma*x3.^5+ff2*cos(W2*t)+u2;

de1=dx3-dx1;
de2=dx4-dx2;

e1 = x3-x1;   
e2= x4-x2;

de1=e2+u1;
de2=-alpha*e2-omegaf*e1-beta*e1*s1- gamma*e1*s2+ff2*cos(W2*t)-ff1*cos(W1*t)+u2;


 dy = [dx1; dx2; dx3; dx4];
end

[prajith samraj]

i need e1 and e2 graph. what can i do?

[Lateef Adewale Kareem]

e1 = y(:,3)-y(:,1); 
e2= y(:,4)-y(:,2); 

Answer 1

[Sam Chak]

Hi @prajith samraj

Try manipulating the parameters to get different results.

% Solver
tspan  = [0 20];  
x10    = 0.11; 
x20    = 0.1;  
x30    = 0.21; 
x40    = 0.2;
y0     = [x10; x20; x30; x40];
[t, y] = ode45(@(t, y) f(t, y), tspan, y0); 

% Plots
e1     = y(:, 3) - y(:, 1);
e2     = y(:, 4) - y(:, 2);
subplot(2,1,1)
plot(t, e1), grid on, xlabel('t'), ylabel('e_{1}')
subplot(2,1,2)
plot(t, e2), grid on, xlabel('t'), ylabel('e_{2}')

function dy = f(t, y) 
    % parameters
    alpha  = 0.5;
    omegaf = -1;
    beta   = 0.8790;
    gamma  = 0.3000;
    W1     = 1.4450;
    ff1    = 0.5381;
    W2     = 1.4450;
    ff2    = 0.5381;
    
    % assignment
    x1 = y(1);    
    x2 = y(2);   
    x3 = y(3);    
    x4 = y(4); 
    e1 = x3 - x1;   
    e2 = x4 - x2;
    s1 = x3^2 + x1*x3 + x1^2;
    s2 = x1^4 + (x1^3)*x3 + (x1^2)*(x3^2) + (x1^2)*(x3^2) + x1*(x3^3) + x3^4;
    u1 = - e2 - e1;
    u2 = beta*e1*s1 + gamma*e1*s2 + omegaf*e1 - ff2*cos(W2*t) + ff1*cos(W1*t);
    
    % sys I
    dx1 = x2;
    dx2 = - alpha*x2 - omegaf*x1 - beta*x1^3 - gamma*x1^5 + ff1*cos(W1*t);
    
    % sys II
    dx3 = x4 + u1;
    dx4 = - alpha*x4 - omegaf*x3 - beta*x3^3 - gamma*x3^5 + ff2*cos(W2*t) + u2;
    de1 = dx3 - dx1;
    de2 = dx4 - dx2;

    dy = [dx1; dx2; dx3; dx4];
end

[prajith samraj]

i need the value of e1dot and e2 dot graph

[Sam Chak]

@prajith samraj, I'm a little confused now. In your comment, you clearly mentioned that you need e1 and e2 graph. Perhaps, you unintentionally confused yourself with e1dot and e2dot?

Please edit the title of your question for clarity...