Coupling schemes for cluster synchronization in coupled Josephson equations

We propose an approach to constructing different coupling schemes to stabilize selected cluster synchronization patterns for coupled Josephson equations. In particular, we select a coupling scheme to create synchronization with frequency ratio m 1 : m 2 : ⋯ : m n , which can be arbitrarily chosen and is independent of the frequencies of the uncoupled oscillators. We also discuss coupled discrete systems.