Coexistence phenomenon refers to the absence of expected tongues of instability in parametrically excited systems. In this paper we obtain sufficient conditions for coexistence to occur in the generalized Ince equation: (1 + a1 cos t+ a2 cos 2t) v̈ +(b1 sin t+ b2 sin 2t) v̇ +(δ + c1 cos t+ c2 cos 2t) v = 0 The results are applied to the stability of motion of a nonlinear normal mode, the x-mode, ...

A dynamic system of the three resonantly coupled waves, two of which are parametrically excited, is investigated. It is shown that when the pump amplitude is increased in this system, a strange attractor (analogous to the known Lorentz attractor) is produced and corresponds to stochastic self-oscillations of the wave amplitudes, yet the phases are always fully correlated. A concrete realization...

Abstract The response of a parametrically excited cantilever beam (PECB) with tip mass is investigated in this paper. paper mainly focused on accurate prediction the system, particular, its hardening and softening characteristics when linear damping considered. First, method varying amplitudes (MVA) multiple scales (MMS) are employed. It shown that both Duffing nonlinearity nonlinear inertia te...

Abstract—In this study, we investigate synchronization in complex network with two hubs by using parametrically excited van der Pol oscillators with parameter mismatch. By means of computer simulation, we confirm various change of synchronization probability in complex network, and observe effects on synchronization probability by changing structural metrics (degree and path length) in a subset...