Synchronization of coupled benchmark oscillators: analysis and experiments

Synchronization is a significant phenomenon in understanding the collective dynamics of coupled oscillators. It is important to know about the behavior and derive sufficient conditions that yield synchronization in coupled benchmark oscillators. The paper aims at achieving synchronization in two types of second-order coupled oscillators, namely the Van der Pol and the Fitzhugh Nagumo oscillators. The oscillators are coupled diffusively with uniform and non-uniform couplings. Initially, the network topology is taken as all-to-all connected, and its synchronization analysis is carried out using the quadratic Lyapunov approach. The algebraic graph theory is used to formulate a quadratic Lyapunov function to attain synchronization of the coupled oscillatory network with the arbitrarily connected network topologies of these oscillators. The couplings used are for both the states as well as for a single state. In each of the above cases, the synchronization is achieved by obtaining sufficient coupling gain. The synchronization has also been demonstrated experimentally for all-to-all and star networked oscillators. The analytical and experimental results have been compared for sufficient coupling gains. Also, the findings are supported by numerical simulation.