Bifurcation of modes in three-coupled oscillators with the increase of nonlinearity

In this paper we investigate bifurcations of modes in three-coupled oscillators with hard and soft nonlinearity in relation to the increase of parameter ε, showing the degree of nonlinearity. The stability of modes in such a system for small ε was already analyzed via averaging theory. Therefore, we start from the stable modes for small ε, and increase ε gradually to observe bifurcations of modes. Through numerical analysis using the shooting method, Runge Kutta method and fast Fourier transforms, we have clarified how the modes (the same-phase, the reverse-phase, the double and triple modes) which exist for small ε, bifurcate when ε becomes larger.