In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method...

We study the possibility of constructing non-BPS charged black holes in 5D Poincare supergravity by partially violating superconformal Killing spinor equations. However, solutions to these modified first order equations are inconsistent with the second order equations of motion beyond the near horizon region. Instead we find, for special prepotentials, that the consistent asymptotically flat ex...

For the representation of eigenstates on a Poincare section at the boundary of a billiard different variants have been proposed. We compare these Poincare Husimi functions, discuss their properties, and based on this select one particularly suited definition. For the mean behavior of these Poincare Husimi functions an asymptotic expression is derived, including a uniform approximation. We estab...

Poincare polinomials of hyperbolic Lie algebras, which are given by HA2 and HA3 in the Kac’s notation, are calculated explicitly. The results show that there is a significant form for hyperbolic Poincare polinomials. Their explicit forms tend to be seen as the ratio of a properly chosen finite Poincare polinomial and a polinomial of finite degree. To this end, by choosing the Poincare polinomia...

Abstract: In this paper, the nonlinear dynamical behaviors of an active magnetic bearing-rotor system are investigated using numerical simulation. Firstly, the nonlinear magnetic force is obtained by Taylor series. Secondly, the primary-internal resonance of an AMBRS(active magnetic bearing) -rotor system is studied with the help of LungKutta method. To analyze the motion characters of system, ...

Poincare half-maps can be used to characterize the behavior of recurrent dynamical systems. Their usefulness is demonstrated for a linear three-dimensional single-loop feedback system. In this example everything can be calculated analytically. The resulting half-maps are "benign" endomorphic maps with a complicated topological structure. This is surprising since the combination of two such half...

BACKGROUND Poincare plots are commonly used to study the nonlinear behavior of physiologic signals. The aim of this study is to evaluate the Poincare plot indices of human heart rate signals during meditation. METHODS For this purpose, heart rate time series of eight Chi meditators available in Physionet database were used. Poincare plots with lags of 1 and 6 were constructed, and the ratio o...

Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. A semi-analytical method of constructing the series solution up to an arbitrary order for relative motion near equilibrium systems is proposed facilitate design formations based on a Lindstedt–Poincaré method. The details expansion and coefficient $$m\!:\!n$$ -period orbits are discussed. To...

A nonlinear Poincare sphere method for measuring polarization-mode dispersion (PMD) using the four-wave mixing (FWM) effect in single-mode optical fibers is presented. This method is based on the FWM-power transfer function on the polarization states of the input signals. Average PMD can be obtained by using this method with measurements in just a narrow optical bandwidth.