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.

This paper investigates the 10 m semi anechoic chamber using a new type hybrid EM wave absorber consisted of the grid-ferrite and the open-top hollow pyramidal EM wave absorber. We designed a new type hybrid EM wave absorber, which length could be slightly realized 65 cm. The 10 m semi anechoic chamber was constructed in the size of L21.5 mW13.5 mH8.9 m as the result of the ray-tracing simulation using this absorber. Then, the site attenuation in the constructed anechoic chamber was measured by using the broadband calculable dipole antennas. As the result, the maximum deviations between the measured site attenuation and theoretical calculated one were obtained within 3.6 dB in the frequency range of 30 MHz to 300 MHz. It was confirmed the validity of a new type hybrid EM wave absorber. Moreover, it was confirmed that the measured results agree with the ray-tracing simulation results, in which the differences are about 1.5 dB.

In this paper, we propose a control method for the synchronization of chaotic systems that does not require the systems to be connected, unlike existing methods such as that proposed by Pecora and Carroll in 1990. The method is based on the reinforcement learning algorithm. We apply our method to two discrete-time chaotic systems with mismatched parameters and achieve M step delay synchronization. Moreover, we extend the proposed method to the synchronization of continuous-time chaotic systems.