A Note on Analyzing the Stability of Oscillator Ising Machines

The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While prior work on the stability of the so-called Oscillator Ising Machines (OIMs) has used the linearization method, in this letter, we present a complementary method to analyze stability using the second order derivative test of the energy / cost function. We establish the equivalence between the two methods, thus augmenting the tool kit for the design and implementation of OIMs.