Bifurcation in asymmetrically coupled BVP oscillators

BVP oscillator is the simplest mathematical model describing dynamical behavior of the neural activity. The large scale neural network can often be described naturally by coupled systems of BVP oscillators. However, even if two BVP oscillators are merely coupled by a linear element, the whole system exhibits a complicated behavior. In this paper, we analyze coupled BVP oscillators with asymmetrical coupling structure, with each oscillator having a different internal resistance. We present a complete four-dimensional system, which shows a rich variety of bifurcation phenomena, and strange attractors. We calculate bifurcation diagrams and confirm relaxation phenomena in the laboratory experiments. We also briefly report a conspicuous strange attractor