Parametric resonance in the Rayleigh-Duffing oscillator with time-delayed feedback

We investigate the principal parametric resonance of a Rayleigh–Duffing oscillator with time-delayed feedback position and linear velocity terms. Using the asymptotic perturbation method, we obtain two slow flow equations on the amplitude and phase of the oscillator. We study the effects of the frequency detuning, the deterministic amplitude, and the time-delay on the dynamical behaviors, such as stability and bifurcation associated with the principal parametric resonance. Moreover, the appropriate choice of the feedback gain and the time-delay is discussed from the viewpoint of vibration control. It is found that the appropriate choice of the time-delay can broaden the stable region of the non-trivial steady-state solutions and enhance the control performance. Theoretical stability analysis is verified through a numerical simulation.The University of Pretoriahttp://www.elsevier.com/locate/cnsnsai201

The Universal Cardinal Ordering of Fixed Points

We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a corollary. The problem present in the symbolic sequences is solved. There, repeated symbols appear, for example, the R (right), which cannot be distinguished among them as it is not known which R is the rightmost of them all. Therefore, there is a lack of information about the dynamical system. Interestingly enough, it is important to point that this theorem needs no previous information about any other orbit.Comment: 19 pages, 4 figure

Climatology of radar anomalous propagation over West Africa

KAISSASSOU Samuel Abstract A comprehensive examination of 5 years of European Centre for Medium-Range Weather Forecasts (ECMWF) data to determine ducting conditions over West Africa and the computation of statistical distributions of the vertical gradient of refractivity determined from 2 years of radiosonde data over Dakar (14.41°N, 17.26°W), Douala (4.00°N, 9.70°E) and Niamey (13.35°N, 2.03°E) were carried out. It is found that diurnal and seasonal variations of the refractivity of the atmosphere are influenced by air temperature and water vapor pressure fluctuation. Refractivity gradients lower than -0.157 m -1 often result in spurious returned echoes and misinterpretation of radar images such as erroneous precipitation detection. The results obtained show that the local climate has an appreciable influence on the vertical profile of refractivity, especially the seasonal north-south movement of the Inter Tropical Discontinuity which is associated with the alternance of wet and dry seasons over the region. It is found that most of ducts occur in the night, morning (0000, 0600 UTC) and late afternoon (1800 UTC). The occurrence probability of abnormal propagation events, such as ducts, can provide some valuable information about the propagation of electromagnetic waves over West Africa

Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions

We study effects of Kac-Baker long-range dispersive interaction (LRI) between particles on kink properties in the discrete sine-Gordon model. We show that the kink width increases indefinitely as the range of LRI grows only in the case of strong interparticle coupling. On the contrary, the kink becomes intrinsically localized if the coupling is under some critical value. Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI increases for supercritical values of the coupling but remains finite for subcritical values. We demonstrate that LRI essentially transforms the internal dynamics of the kinks, specifically creating their internal localized and quasilocalized modes. We also show that moving kinks radiate plane waves due to break of the Lorentz invariance by LRI.Comment: 11 pages (LaTeX) and 14 figures (Postscript); submitted to Phys. Rev.