This paper develops a design method and theoretical analysis for piecewise nonlinear oscillators that have desired circular limit cycles. Especially, the mathematical proof on existence, uniqueness, and stability of the limit cycle is shown for the piecewise nonlinear oscillator. In addition, the relationship between parameters in the oscillator and rotational directions and periods of the limit cycle trajectories is investigated. Then, some numerical simulations show that the piecewise nonlinear oscillator has a unique and stable limit cycle and the properties on rotational directions and periods hold.

In this letter, we propose a partial impedance-matching method using a two-strip resonator for noncontact Passive Intermodulation (PIM) measurements using a coaxial tube. It is shown that the strip closer to the inner tube of the coaxial tube is dominant in the observed PIM characteristics while both strips are excited equally. The ideal efficiency of power to each strip is 50%, which is a significant improvement in comparison with conventional methods.

Ultrafast all optical switching using pulse trapping by 100 fs ultrashort soliton pulse across zero dispersion wavelength is investigated. The characteristics of pulse trapping are analyzed both experimentally and numerically. Using the pulse trapping, 1 THz ultrafast all optical switching is demonstrated experimentally. Arbitral one pulse is picked off from pulse train. Pulse trapping for CW signal is also demonstrated and ultrashort pulse is generated by pulse trapping. From these investigation, it is shown that ultrafast all optical switching up to 2 THz can be demonstrated using pulse trapping.

Nonlinear behavior of electromagnetic surface waves propagating along a tangentially magnetized ferrite slab is investigated. The nonlinear Schrodinger equation (NLSE) which describes the temporal evolution of the electromagnetic wave pulses has been derived directly from the Maxwell equations and the equation of precessional motion for the magnetization in the ferrite slab with the aid of the reductive perturbation method without magnetostatic approximation. Based on the formula derived, we have numerically evaluated the frequency-dependence of the nonlinear coefficient in the NLSE for both a magnetostatic surface wave mode and a dynamic mode. As a result, we have confirmed the possibility of the propagation of solitons in the waveguide.

In this paper, we clarify fundamental properties of conventional back-propagation neural networks to learn chaotic dynamical systems by some numerical experiments. We train three-layers networks using back-propagation algorithm with the data from two examples of two-dimensional discrete dynamical systems. We qualitatively evaluate the trained networks with two methods analysing geometrical mapping structure and reconstruction of an attractor by the recurrent feedback of the networks. We also quantitatively evaluate the trained networks with calculation of the Lyapunov exponents that represent the dynamics of the recurrent networks is chaotic or periodic. In many cases, the trained networks show high ability of extracting mapping structures of original two-dimensional dynamical systems. We confirm that the Lyapunov exponents of the trained networks correspond to whether the reconstructed attractors by the recurrent networks are chaotic or periodic.