Complete mixed-mode oscillation synchronization in weakly coupled nonautonomous Bonhoeffer–van der Pol oscillators

Abstract

We investigate completely and incompletely synchronized mixed-mode oscillations (MMOs) generated by weakly coupled nonautonomous Bonhoeffer–van der Pol oscillators. We consider two identical oscillators that generate MMOs and MMO-incrementing bifurcations (MMOIBs), connected by a large inductor. Our numerical results indicate that the chaos in these two oscillators cannot be synchronized under such weak coupling. By contrast, completely synchronized MMOIB-generated MMOs appear, which can be induced successively many times. We confirm this complete synchronization by checking the bifurcation equations using Newton’s method to a precision of 10|$^{-13}$|⁠. In addition, we find that incompletely synchronized MMOs appear at the parameter values where chaos is generated when the oscillators are not coupled.