Transient dynamics and chaos observed in strongly nonlinear mutually-coupled oscillators

In this paper, the behavior of the double-mode oscillation in mutually coupled oscillators with hard nonlinear conductance with the increase of ε (=degree of nonlinearity), is investigated. Namely, when ε is increased, the two frequency components of the double-mode oscillation adjust themselves to be a periodic solution via synchronization. In particular, just before the pull-in is achieved, we observed an interesting phenomenon such that two symmetric periodic solutions switch alternately, which in some case, can be chaotic. We elucidate its mechanism by calculating unstable manifolds of degenerate saddles.