The modified FitzHugh–Nagumo system as an oscillator

The use of the modified FitzHugh–Nagumo system is extended to the limit cycle regime. Ranges of parameters for which such oscillatory behavior prevails are calculated and properties of phase space and individual pulses are obtained. Copyright © 2008 John Wiley & Sons, Ltd.     

Chaotic behavior analysis based on corner bifurcations

In this paper, a mathematical analysis in order to generate a chaotic behavior for bounded piecewise smooth systems of dimension three submitted to one of its specific bifurcations, namely the corner one, is proposed. This study is based on period doubling method.     

Example of a suspension bridge ODE model exhibiting chaotic dynamics: A topological approach

Using an elementary phase-plane analysis combined with some recent results on topological horseshoes and fixed points for planar maps, we prove the existence of infinitely many periodic solutions as well as the presence of chaotic dynamics for a simple second order nonlinear ordinary differential equation arising in the study of Lazer-McKenna suspension bridges model.     

PT-Symmetric Solutions of Schrödinger Equation with Position-Dependent Mass via Point Canonical Transformation

PT-symmetric solutions of Schrödinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.     

Cumulative solutions of nonlinear longitudinal vibration in isotropic solid bars

Based on the strain invariant relationship and taking the high-order elastic energy into account, a nonlinear wave equation is derived, in which the excitation, linear damping, and the other nonlinear terms are regarded as the first-order correction to the linear wave equation. To solve the equation, the biggest challenge is that the secular terms exist not only in the fundamental wave equation but also in the harmonic wave equation （unlike the Duffing oscillator, where they exist only in the fundamental wave equation）. In order to overcome this difficulty and to obtain a steady periodic solution by the perturbation technique, the following procedures are taken： （i） for the fundamental wave equation, the secular term is eliminated and therefore a frequency response equation is obtained; （ii） for the harmonics, the cumulative solutions are sought by the Lagrange variation parameter method. It is shown by the results obtained that the second- and higher-order harmonic waves exist in a vibrating bar, of which the amplitude increases linearly with the distance from the source when its length is much more than the wavelength; the shift of the resonant peak and the amplitudes of the harmonic waves depend closely on nonlinear coefficients; there are similarities to a certain extent among the amplitudes of the odd- （or even-） order harmonics, based on which the nonlinear coefficients can be determined by varying the strain and measuring the amplitudes of the harmonic waves in different locations.     

双波长光参量振荡器的研究进展及应用

双波长光参量振荡器是一类非常新颖的激光器件。本文阐述了双波长光参量振荡器的工作原理,并总结了双波长光参量振荡器的研究进展,探讨了双波长光参量振荡器发展中存在的技术问题,介绍了双波长光参量振荡器的应用。     

Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C_2v$C_{2v}$ exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry.     

基于光电振荡器的宽带射频下转换及在高清视频传输的应用

以无压缩全高清视频的光载无线传输为背景,通过研究宽带射频光子下转换技术,从而构建全高清视频的实时传输系统,其中下转换系统主要基于光电振荡器实现.由于光电振荡器的注入锁定,光微波信号中的载波信号被提取出来,并反馈至调制器,与宽带光微波信号混频,在光域实现信号下转换.实验论证了载频为10GHz,码率大于2Gb/s的信号下转换和有线无线传输.利用天线和光纤实现了距离为0.5m的无线分发和距离为10km的有线传输.本文还成功实现了1.5Gb/s无压缩高清视频信号的实时传输.实验结果表明,该系统具有大带宽、抗电磁干扰等优点,同时利用光电振荡器的自动相位跟踪技术,无须外加锁相等操作.整个下转换系统简单稳定,为高清视频的有线无线传输提供了论证和演示平台.     

Comments on “Design of sliding mode controller for a class of fractional-order chaotic systems” [Commun Nonlinear Sci Numer Simulat 17 (2012) 356-366]

Some comments on the paper [Yin C, Zhong S-M, Chen W-F. Design of sliding mode controller for a class of fractional-order chaotic systems. Commun Nonlinear Sci Numer Simulat 17 (2012) 356-366] are pointed out in this note. Besides, recently introduced fractional-order Lyapunov stability theorems are used to prove the finite-time occurrence of the sliding motion.