In many applications such as fluid or solid modeling, chaotic noise may be cumbersome. Instead of estimating the Lyapunov exponent of the system, one may be interested in measuring the amplitude of the system’s chaotic noise in a unit better suited to the application, e.g., the amplitude (in mm) of the vibration of a solid’s surface. The goal of this study is to propose a method to achieve this...

In this paper, the periodic, quasi periodic and chaotic responses of rotational machines with a hexagonal centrifugal governor are studied. The external disturbance is assumed as a sinusoid effect. By using the forth order Rung-Kutta numerical integration method, bifurcation diagram, largest Lyapunov exponent and Lyapunov dimension are calculated and presented to detect the critical controlling...

The study of chaotic phenomena in partial differential equations is a challenging subject. In this paper, we survey the recent progress in the study of chaotic vibration of the linear wave equation with nonlinear boundary feedback control law. We show that when there is linear energy injection at one end of the boundary and the self-regulating or van der Pol nonlinearity at the other end of the...

By using dissipative system Lagrange equation, the strongly nonlinear dynamic equation of torsional vibration system is deduced, which contains a class of square and cube nonlinear rigidity and combination harmonic excitations. Bifurcation characteristics of the strongly nonlinear system are analyzed in the autonomous and non-autonomous situations by means of singular point stability theory and...

Abstract. We investigate geometric phase of fermion states under relative vibrations of two sublattices in graphene by solving time-dependent Schödinger equation using Floquet scheme. In a period of vibration the fermions acquire different geometric phases depending on their momenta. There are two regions in the momentum space: the adiabatic region where the geometric phase can be approximated ...