Horseshoe chaos and subharmonic orbits in the nanoelectromechanical Casimir nonlinear oscillator

Abstract

The progressive miniaturization of electronic components today makes feasible to exploit the nanoscale level. At this scale, phenomena peculiar of the quantum world arise, which can be exploited to realize innovative and potential breakthrough devices. In this paper, the dynamic behavior of one such device, the Casimir nonlinear oscillator is analyzed. Using the Melnikov's method, we prove that under the effect of a weak damping and a weak periodic forcing, complex behaviors in the form of Smale's horseshoes arise, and the mechanism leading to their birth is revealed. In Figure 7, two limit cycles, which coexist for x = 4, o = 1, eg = 0.1, and eA = 0.02 are shown. The small cycle on the right, which corresponds to the hyperbolic saddle point of the Poincaré map 600 M. BONNIN J Figure 7. Two coexisting limit cycles for x = 4, o = 1, eg = 0.1, and eA = 0.02. Floquet's multipliers are: for the left limit cycle l 1 = 1, l 2, 3 = 0.4580 AE i0.5690; for the right cycle m 1 = 1, m 2 = 0.0014, and m 3 = 391.6301. HORSESHOE CHAOS AND SUBHARMONIC ORBITS IN CASIMIR OSCILLATOR 601

Nonlinear Actuation Dynamics of Driven Casimir Oscillators with Rough Surfaces

“…The general non-autonomous case, which is closer to an experimental MEMS oscillator setup, has been tackled analytically for ideal metals [21], as well as using an expansion of the Casimir force in the oscillator's coordinates [10,22]. The higher order terms in such polynomial expansions give rise to additional zeros of the conservative force equation, which do not correspond to physical equilibria [22]. Our approach does not rely on any such approximations, and includes the Casimir force at submicron-scale separations in an experimentally relevant way [11,14].…”