Stick-slip chaos detection in coupled oscillators with friction

We consider two coupled oscillators with negative Duffing type stiffness which are self (due to friction) and externally (harmonically) excited. The fundamental solutions of the homoclinic orbit are constructed. Then, the Melnikov–Gruendler approach is used to define the Melnikov’s function including smooth and stick-slip chaotic behaviour. Theoretical considerations are supported by numerical examples.