How do I exclude the first ten observations in the line plot generated by the three differential equations

close all
clear all
clc
tspan   = [0 100];
y0      =  0.7;   % initial value of state variable x1
r0      =  0.7;   % initial value of state variable x2
w0      =  0.8;   % initial value of state variable x3
x0      = [y0; r0; w0];
[t, x]  = ode45(@odefcn, tspan, x0);

%% Plot x2 (y-axis) vs. x1 (x-axis)
subplot(3,1,1);
plot(t,x(:,1));
xlabel('Time')
ylabel('Output');
subplot(3,1,2);
plot(t,x(:,2));
xlabel('Time')
ylabel('Policy Rate');
subplot(3,1,3);
plot(t,x(:,3));
xlabel('Time')
ylabel('Wage Share');

y0 = [0.7; 0.7; 0.8];

%% System of three differential equations
function dx = odefcn(t, x)
% definitions
y       = x(1);
r       = x(2);
w       = x(3);
% parameters
alpha   = 1.0;
beta    = 1.0;
gamma   = 0.1;
delta   = 0.3;
mu      = 1.0;
lambda  = 0.3;
theta   = 0.1;
omega   = 0.2;
% ODEs
dx(1,1) = alpha * y - beta * r * y;
dx(2,1) = - omega * r + gamma * w * r + delta * y * r;
dx(3,1) = - theta * w + lambda * y * w - mu * w * w;
end

[Christopher]

Line plot of the differntial equations.

[Torsten]

@Christopher

You really mean the first ten outputs from ode45 or the outputs up to time t = 10 ?

[Christopher]

I want to fit a trend line through the data excluding the first ten periods. I want to show that there is no trend in the data after those periods.

[Torsten]

I want to fit a trend line through the data excluding the first ten periods.

What are "periods" according to your definition ? According to what "period" usually means, your graphs only have 6 or 7 periods for tspan = [0 100] (counted as the number of minima/maxima of the plotted functions).

[Christopher]

I was thinking in terms of timespan...

[Torsten]

It's still not clear what you mean.

If you define

tspan   = [0 100];

ode45 will choose the output times between 0 and 100 on its own. Thus excluding the first ten outputs does not tell you anything about the time points when these ten outputs were reported: they could be [0 1 2 3 4 5 6 7 8 9] or any other increasing vector with 10 elements starting at 0.

Answer 1

[Matt J]

One way,

tspan   = [0 100];
y0      =  0.7;   % initial value of state variable x1
r0      =  0.7;   % initial value of state variable x2
w0      =  0.8;   % initial value of state variable x3
x0      = [y0; r0; w0];
[t, x]  = ode45(@odefcn, tspan, x0);

x(1:10,:)=nan;

[Steven Lord]

And once you've replaced the first ten points with NaN, consider using the detrend function, the trenddecomp function, or the Find and Remove Trends Live Editor Task.

[Adam Danz]

Alternatively, if you'd like to preserve the initial 10 values,

plot(t(11:end),x(11:end,1));

[Christopher]

@Adam Danz Thats exacrtly what I am trying to do! I was able to run the code, but it did not change the starting point for the plot.

[Matt J]

@Christopher Cerainly it does. How Could it not? But see below:

tspan   = [0 100];
y0      =  0.7;   % initial value of state variable x1
r0      =  0.7;   % initial value of state variable x2
w0      =  0.8;   % initial value of state variable x3
x0      = [y0; r0; w0];
[t, x]  = ode45(@odefcn, tspan, x0);

%% Plot x2 (y-axis) vs. x1 (x-axis)
h=plot(t,x(:,1),'r', t(11:end),x(11:end,1),'b-'); xlim([0,25])

●

[Christopher]

Ok, use the same code to generate x2 and x3?

[Matt J]

Yes, I would imagine.