what the problem that I get to during plotting the graph

ti = 0;

tf = 10E-4;

tspan=[ti tf];

y0=[10;10;1;1;1].*10E-2;

[T,Y]= ode45(@(t,y) rate_eq(t,y),tspan,y0);

plot(T,Y(:,1));

xlim([0 4E-4])

ylim([0 8])

xlabel('time')

ylabel('amplitude')

yyaxis right

ylabel('phase difference')

hold on

plot(T,((Y(:,5))./6.28));

hold off

function dy = rate_eq(t,y)

dy = zeros(5,1);

o = 2E5;

tc = 30E-9;

tf = 230E-6;

a1 = 0.1;

a2 = 0.1;

P1 = 0.2;

P2 = 0.2;

kc = 3E-3;

s = 0.17;

k = s.*kc;

dy(1) = ((y(3) - a1) * y(1) + k * y(2) * cos(y(5))) / tc;

dy(2) = ((y(4) - a2) * y(2) + k * y(1) * cos(y(5))) / tc;

dy(3) = (P1 - y(3) * (y(1)^2 + 1)) / tf;

dy(4) = (P2 - y(4) * (y(2)^2 + 1)) / tf;

dy(5) = o - k / tc * (y(1) / y(2) + y(2) / y(1) * sin(y(5)));

end

I have marked the circle which part is not proper waveform and I need a proper waveform with same amplitude, I need to know what is causing this, is it the constant value which I have given , initial conditions or something

and please check that if I solve the differential equation correctly or not, I mean the techinques that I apply to solve this differential equation.

these are the differential equation

y(1) = A1

y(2) = A2

y(3) = G1

y(4) = G2

y(5) = Φ

Answer 1

[VBBV]

ti = 0;
tf = 10E-4;
tspan=[ti tf];
y0=[2;2;1;1;1].*10E-2;  % this change 
[T,Y]= ode45(@(t,y) rate_eq(t,y),tspan,y0);
plot(T,Y(:,1));
xlim([0 4E-4])
ylim([0 8])
xlabel('time')
ylabel('amplitude')
yyaxis right
ylabel('phase difference')
hold on
plot(T,((Y(:,5))./6.28));
hold off

function dy = rate_eq(t,y)
dy = zeros(5,1);
o = 2E5;  
tc = 30E-9;  
tf = 230E-6;  
a1 = 0.1;
a2 = 0.1;
P1 = 0.2;  
P2 = 0.2;
kc = 3E-3;
s =  0.17;
k = s.*kc;
dy(1) = ((y(3) - a1) * y(1) + k * y(2) * cos(y(5))) / tc;
dy(2) = ((y(4) - a2) * y(2) + k * y(1) * cos(y(5))) / tc;
dy(3) = (P1 - y(3) * (y(1)^2 + 1)) / tf;
dy(4) = (P2 - y(4) * (y(2)^2 + 1)) / tf;
dy(5) = o - k / tc * (y(1) / y(2) + y(2) / y(1) * sin(y(5)));
end

Yes, the constant values given as initial conditions need to be modified to get proper waveform.

[SAHIL SAHOO]

I couln't found any suitable initial condition for which the waveform is proper and please can you check if my algorithm is correct for solving the differential equation that I gave you in the picture.

[Torsten]

dy(5) doesn't coincide with your equation in the picture.

And we don't know whether I1 = y(1)^2 and I2 = y(2)^2.

ti = 0;
tf = 10E-4;
tspan=[ti tf];
y0=[10;10;1;1;1].*10E-2;  % this change 
options = odeset('RelTol',1e-8,'AbsTol',1e-8);
[T,Y]= ode45(@(t,y) rate_eq(t,y),tspan,y0,options);
plot(T,Y(:,1));
xlim([0 4E-4])
ylim([0 8])
xlabel('time')
ylabel('amplitude')
yyaxis right
ylabel('phase difference')
hold on
plot(T,((Y(:,5))./6.28));
hold off

function dy = rate_eq(t,y)
dy = zeros(5,1);
o = 2E5;  
tc = 30E-9;  
tf = 230E-6;  
a1 = 0.1;
a2 = 0.1;
P1 = 0.2;  
P2 = 0.2;
kc = 3E-3;
s =  0.17;
k = s.*kc;
dy(1) = ((y(3) - a1) * y(1) + k * y(2) * cos(y(5))) / tc;
dy(2) = ((y(4) - a2) * y(2) + k * y(1) * cos(y(5))) / tc;
dy(3) = (P1 - y(3) * (y(1)^2 + 1)) / tf;
dy(4) = (P2 - y(4) * (y(2)^2 + 1)) / tf;
dy(5) = o - k / tc * (y(1) / y(2) + y(2) / y(1)) * sin(y(5));
end