Galloping: nonlinear oscillation in a periodically forced loaded hanging cable

Nonlinear Waves in Transmission Lines Periodically Loaded with Tunneling Diodes

Oscillation criteria for a forced second order nonlinear dynamic equation

In this paper, we will establish some new interval oscillation criteria for forced second-order nonlinear dynamic equation (p(t)x(t)) + q(t)|xσ(t)|γsgn x(t) = f(t), t ∈ [a, b], on a time scale T where γ ≥ 1. As a special case when T = R our results not only include the oscillation results for second-order differential equations established by Wong (J. Math. Anal. Appl., 231 (1999) 233-240) and ...

Phase Model Reduction and Synchronization of Periodically Forced Nonlinear oscillators

Phase models represent the ideal framework to investigate the synchronization of a nonlinear oscillator with an external forcing. While many researches focused the attention to their analysis, little work has been done about the reduction of a physical system to the corresponding phase model. In this paper we show how, resorting to averaging techniques, it is possible to obtain the phase model ...

Periodically Forced Hopf Bifurcation

We study a periodically forced system of ODEs near a point of Hopf bifurcation, where the forcing frequency ωF is near the Hopf frequency ωH and the forcing amplitude ε is small. We assume that in this system only the forcing frequency is varied and we determine all small amplitude periodic solutions of the forced system that have frequency ωF . In other words, we examine the influence of the f...

Oscillation of Solutions to Nonlinear Forced Fractional Differential Equations

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...