Averaging method analysis of a new mutual synchronization method from living organism

In this paper, we propose averaging method in analyzing two mutually-coupled van der Pol oscillators with a new coupling scheme from living organism. This scheme was invented by S. Nagano, and its characteristic existed in the special nonlinear coupling which was completely different from the conventional linear coupling. Unfortunately, only computer simulation results are given so far. We clarify that this system can be reduced to the simpler averaged equation, and that synchronization range can be obtained theoretically by investigating the stability of the equilibrium point of the averaged equation. As a result, we confirm theoretically that synchronization range of this scheme is much larger than conventional scheme, and hence superior to it