Network Synchronization of Linear Non-Minimum Phase Oscillators: A Motivating Example

This paper investigates the onset of synchronization in a network of linear non-minimum phase oscillators. We provide a prototype example which illustrates that full synchronization in such oscillator network under diffusive coupling may appear for only limited coupling strength, but, when the coupling is extended to a linear dynamic one, the synchronization appears for sufficiently large coupling. Also, the example at hand shows that if the coupling strength is fixed, there exists a limitation on the maximum number of nodes that can be synchronized when using diffusive couplings. In contrast, dynamic coupling allows removing such limitation. The obtained theoretical results are illustrated by computer simulations.