Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry

• The dynamic behavior of a cyclic symmetric chain of nonlinear oscillator is studied.
• A nonlinear damping with polynomial form is used.
• Multiple localized solutions have been found.
• Superposing the system solutions a “snaking-like” structure appears.
• Snaking is well known in different physic fields, but not yet in vibrating systems.

Snaking bifurcations in a chain of mechanical oscillators are studied. The individual oscillators are weakly nonlinear and subject to self-excitation and subcritical Hopf-bifurcations with some parameter ranges yielding bistability. When the oscillators are coupled to their neighbours, snaking bifurcations result, corresponding to localised vibration states. The snaking patterns do seem to be more complex than in previously studied continuous systems, comprising a plethora of isolated branches and also a large number of similar but not identical states, originating from the weak coupling of the phases of the individual oscillators.