Making ODE45 stop at periodic solutions?

I am working with a Duffin oscillator:

% Recover Quadcopter variables
z    = State(1,1);
w    = State(2,1);

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F(1,1)     = w;
F(2,1)     = epsilon*cos(omega_rho*t)-k0*z-k1*z^3-f0*w;

I wanted to find the exsistance and stability of periodic solutions. For that I wanted to evaluate the system with ODE45 and create an event that stops the integration when a periodic/quasi-periodic solution is found, but the basic event locator seems like it cnnot do it, since it cannot evaluate previous states of the solution. I have also read about Delay Differential Equation solvers and event locators, but someone said that it did not work well with quasi-periodic solutions, which I need. Is there a way to do this? If it is done using DDEs, how exactly?

Answer 1

[Abhisek Pradhan]

Event Functions can be used to determine an appropriate time to stop the solution but it does have few limitations.

Delay Differential solvers should work good for this scenario if the appropriate solver is selected.

Refer the following link to know more about Delay differential solvers, types of solvers and where they can be used.

https://www.mathworks.com/help/matlab/delay-differential-equations.html

Refer this for examples on solving Delay differential equations.