The stability, instability, and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point is studied in detail. The critical point is characterized by two distinct pairs of pure imaginary eigenvalues of the Jacobian, and the system is described by two independent parameters. The analysis is based on a generalized perturbation procedure which employs mul...

This paper reports a novel four-degrees-of-freedom (DOF) nonresonant micromachined gyroscope design concept that addresses two major MEMS gyroscope design challenges: eliminating the mode-matching requirement and minimizing instability and drift due to mechanical coupling between the drive and sense modes. The proposed approach is based on utilizing dynamical amplification both in the 2-DOF dri...

Hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps CARS) is employed for quantitative gas-phase temperature measurements in combustion processes and heated flows. In this approach, ultrafast 100-fs laser pulses are used to induce vibrational and rotational transitions in N2 and O2, while a third spectrally narrowed picosecond pulse is used to probe the molecular response...

We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov–Schmidt reduction and a Nash–Moser iteration scheme.

We are concerned with the persistence of frequency of invariant tori for analytic integrable Hamiltonian system with quasiperiodic perturbation. It is proved that if the unperturbed system satisfies the Rüssmann’s nondegeneracy condition and has nonzero Brouwer’s topological degree at someDiophantine frequency; the perturbed system satisfies the colinked nonresonant condition, then the invarian...

In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator ẍ+ f(ẋ) + ax − bx− = φ(t, x), where a and b are positive constants satisfying the nonresonant condition 1 √ a + 1 √ b / ∈ Q and φ(t, x) is 2π−periodic in the first variable and bounded.