There's Plenty of Room in Higher Dimensions: Internal Resonance and Decision Mechanisms in Mechanical Resonators
Abstract: To understand how adaptive behavior emerges in living and artificial systems is a major challenge for science. In this talk, I consider something simpler — dead vibrating silicon beams and graphene membranes. I will give a short introduction to nonlinear dynamics of vibrational modes in mechanical resonators. An interesting situation occurs when two vibrational modes have a rational relation between their frequencies — a so-called internal resonance. The match in frequency allows for efficient transfer of energy between the two modes. Hence, the internal resonance will strongly affect both the dissipation and the driven response of the resonator. The complex response has similarities with other strongly nonlinear systems such as interacting neurons in the brain. Furthermore, the driven response may exhibit choice mechanisms leading to stochastic switching between different long-term behaviors. In future work, we plan to experimentally control this switching as a means to achieve primitive adaptive behavior in mechanical resonators.