There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...

We propose in this paper a self-referenced method based on asynchronous sampling to monitor the waveform of periodic and quasi-periodic signals, with a low number of samples, typically 214 or lower. It provides a high-resolution representation of the signal under test, representative of the analog intensity signal under test. Additionally, the proposed approach is robust to the timin...

Non-linear behaviors of a single neuron described by Fitzhugh-Nagumo (FHN) neuron model, with external electromagnetic radiation considered, is investigated. It is discovered that with external electromagnetic radiation in form of a cosine function, the mode selection of membrane potential occurs among periodic, quasi-periodic, and chaotic motions as increasing the frequency of external transme...

Many numerical problems arising in modern photonic and electromagnetic applications involve the scattering of a plane wave from a piecewise-homogeneous medium, periodic in one direction. Boundary integral equations are an efficient approach to solving such boundary-value problems with high-order convergence. The standard way to periodize is then to replace the free-space Green’s function kernel...

Superfluids with a tendency towards periodic order have both phonon- and rotonlike spectra. We show that magnetoroton softening occurs in 87Rb spinor condensates. A rich variety of dynamical instabilities emerges as a function of the magnetic field orientation and strength of the quadratic Zeeman shift. These instabilities are driven by an effective dipolar interaction modified dramatically by ...

A simple discrete recurrent neural network model is considered. The local stability is analyzed with the associated characteristic model. In order to study the quasi-periodic orbit dynamic behavior, it is necessary to determinate the Neimark-Sacker bifurcation. In the case of two neurons, one necessary condition that produces the Neimark-Sacker bifurcation is found. In addition to this, the sta...

In this paper, we make a detailed study of the spin-orbit dynamics of Mercury, as predicted by the realistic model which has been recently introduced in a series of papers mainly by Efroimsky and Makarov. We present numerical and analytical results concerning the nature of the librations of Mercury’s spin in the 3:2 resonance. The results provide evidence that the librations are quasi-periodic ...

We prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in Z is stable under localized time-quasi-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The main tools are the Fröhlich-Spencer mechanism for the random component and the Bourgain-Goldstein-Schlag mechanis...