Why do I receive error stating that function needs to appear at the end of the file? MATLAB Differential Equations Help

May someone help me figure out why I keep getting the error at the end of this message?

global alpha 
global beta
% Y = [x(t) y(t)], Y(1) = x(t), Y(2) = y(t)
function [dx_dt dy_dt] = odefun(t, Y)
x = Y(1); y = Y(2);
global alpha
global beta
dx_dt = beta * (1 - x - y) * x - alpha * x;
dy_dt = alpha * x;
end

alpha = 0.1;
beta = 0.1;
for x0 = [0:0.05:0.5]
    alpha = 0.1
    beta = 0.1
    fig = figure;
    [t_array, Y_array] = ode45(odefun, [0:200], [x0 0]);
    plot(t_array, Y_array)
end
alpha = 0.05;
beta = 0.2;
for x0 = [0:0.05:0.5]
    fig = figure;
    [t_array, Y_array] = ode45(@odefun, [0:200], [x0 0]);
    plot(t_array, Y_array)
end

Error: File: projectF.m Line: 11 Column: 1

Function definitions in a script must appear at the end of the file.

Move all statements after the "odefun" function definition to before the first local function

definition.

Answer 1

[Walter Roberson]

It is just a Fact Of Life with MATLAB. You have some non-function statements, then you define a function, then you end the function, then you have more non-function statements. MATLAB considers your script (the original non-function statements) to have ended as soon as the first function definition appeared, and doesn't know what to do with the non-function statements after the function definition. Just move the function definition to the end.

global alpha 
global beta
% Y = [x(t) y(t)], Y(1) = x(t), Y(2) = y(t)


alpha = 0.1;
beta = 0.1;
for x0 = [0:0.05:0.5]
    alpha = 0.1
    beta = 0.1
    fig = figure;
    [t_array, Y_array] = ode45(odefun, [0:200], [x0 0]);
    plot(t_array, Y_array)
end

alpha = 0.1000

beta = 0.1000

Not enough input arguments.

Error in solution>odefun (line 24)
x = Y(1); y = Y(2);

alpha = 0.05;
beta = 0.2;
for x0 = [0:0.05:0.5]
    fig = figure;
    [t_array, Y_array] = ode45(@odefun, [0:200], [x0 0]);
    plot(t_array, Y_array)
end

function [dx_dt dy_dt] = odefun(t, Y)
x = Y(1); y = Y(2);
global alpha
global beta
dx_dt = beta * (1 - x - y) * x - alpha * x;
dy_dt = alpha * x;
end

[Walter Roberson]

The insufficient inputs is because you had ode45(odefun, [0:200], [x0 0]) -- that syntax invokes odefun with no parameters and expects odefun to return a function handle. You want to instead pass a handle to odefun

global alpha 
global beta
% Y = [x(t) y(t)], Y(1) = x(t), Y(2) = y(t)


alpha = 0.1;
beta = 0.1;
for x0 = [0:0.05:0.5]
    alpha = 0.1
    beta = 0.1
    fig = figure;
    [t_array, Y_array] = ode45(@odefun, [0:200], [x0 0]);
    plot(t_array, Y_array)
end

alpha = 0.1000

beta = 0.1000

Error using odearguments
ODEFUN returns a vector of length 1, but the length of initial conditions vector is 2. The vector returned by ODEFUN and the initial conditions vector must have the same number of elements.

Error in ode45 (line 104)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

alpha = 0.05;
beta = 0.2;
for x0 = [0:0.05:0.5]
    fig = figure;
    [t_array, Y_array] = ode45(@odefun, [0:200], [x0 0]);
    plot(t_array, Y_array)
end

function [dx_dt dy_dt] = odefun(t, Y)
x = Y(1); y = Y(2);
global alpha
global beta
dx_dt = beta * (1 - x - y) * x - alpha * x;
dy_dt = alpha * x;
end

[Walter Roberson]

You cannot return multiple derivatives on the left side of an ode function. You need to return a column vector as the single output of the ode function. (There might potentially be other outputs as well, depending on options you have configured.)

global alpha 
global beta
% Y = [x(t) y(t)], Y(1) = x(t), Y(2) = y(t)


alpha = 0.1;
beta = 0.1;
for x0 = [0:0.05:0.5]
    alpha = 0.1
    beta = 0.1
    fig = figure;
    [t_array, Y_array] = ode45(@odefun, [0:200], [x0 0]);
    plot(t_array, Y_array)
end

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.1000

beta = 0.1000

alpha = 0.05;
beta = 0.2;
for x0 = [0:0.05:0.5]
    fig = figure;
    [t_array, Y_array] = ode45(@odefun, [0:200], [x0 0]);
    plot(t_array, Y_array)
end

function [dxdy_dt] = odefun(t, Y)
x = Y(1); y = Y(2);
global alpha
global beta
dx_dt = beta * (1 - x - y) * x - alpha * x;
dy_dt = alpha * x;
dxdy_dt(1,1) = dx_dt;
dxdy_dt(2,1) = dy_dt;
end

[Tahirah]

Oh I understand now, with the function being at the end. Thank you so much for your help!