write a function which mimics odetovectorfield in matlab

To write a function that mimics the odetovectorfield function in MATLAB, you can create a custom function that takes the time variable and state vector as inputs and returns the derivative vector.

Here is an example of how you can write such a function:

main.m
function dxdt = vectorField(t, x)
    % Your vector field equations
    dxdt = zeros(size(x));

    % Define your vector field equations here
    % dxdt(1) = ...
    % dxdt(2) = ...
    % ...

end
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In the function, t is the independent variable (usually time) and x is the state vector (a column vector of the system's variables).

You will need to replace the comment Your vector field equations with the actual equations of your system. For example, if you have a system of two differential equations:

main.m
dx/dt = -0.1*x(1) + 0.2*x(2)
dy/dt = -0.3*x(1) + 0.4*x(2)
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The function should be modified as follows:

main.m
function dxdt = vectorField(t, x)
    % Your vector field equations
    dxdt = zeros(size(x));

    dxdt(1) = -0.1*x(1) + 0.2*x(2);
    dxdt(2) = -0.3*x(1) + 0.4*x(2);

end
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You can then use this function as the input to the ode45 function or any other ODE solver in MATLAB to numerically solve your system of differential equations.

Note that the example above assumes a system of two differential equations. If you have a different number of equations, you will need to modify the size of the dxdt vector accordingly.

Make sure to replace the vector field equations with your own system of equations and adjust the function accordingly.