Behavior of solutions related to an accuracy exp(-1/ε) is studied. Computer results are given, and examined from the view-point of non-standard analysis. The experimental results raise some important questions on the computer study of slow-fast systems.

In this paper, we demonstrate how Yamakawa's chaotic chips and Chua's circuits can be used to implement a secure communication system. Furthermore, their performance for the secure communication is discussed.

Canard is a new phenomenon of slow-fast systems, which was found by the numerical computations. Our primary purpose of this paper is to study the canard from the experimental viewpoint. The following results are obtained by the experimental observation of a nonlinear circuit: (1) Canard really appears in the actual circuit. But canard's life in the circuit is extremely short. (2) When a canard vanished, an irregular oscillations or a cycle with period two is still there, which usually does not occur in the two dimensional autonomous systems.

A new phenomenon of a slow-fast system, canard, is studied. Some interesting propeties and the existence of canards are shown by using non-standard analysis and singular perturbations. There results explain the strange behavior of a nonlinear circuit with a small parameter.

Our primary purpose of this paper is to study attractors and bifurcation phenomenon appearing in an eventually bounded circuit. The secondary purpose is to demonstrate the results obtained from the instruments which display Lorenz maps, Poincaré maps and cross sections of attractors on a synchroscope. The above mentioned circuit contains two non-linear resistors and is written as 3 first order differential equations. Experimental observations show:(a) maximum number of the attractors in three.(b) maximum number of the stable limit cycles is three.(c) maximum number of the chaotic attractor is two.Observed bifurcations are:(a) Hopf bifurcation,(b) period doubling bifurcation,(c) periodic window.Furthermore, we examined the Feigenbaum constant δ experimentally and estimated it at 4.67.

In this paper, chaos synchronization in coupled discrete-time dynamical systems is studied. Computer results display the interesting synchronization behaviors in the mutually coupled systems. As possible applications of chaos synchronization, parameter estimations and secure communications are proposed. Furthermore, a modified OGY method is given, which converts a chaotic motion into a periodic motion.

This paper tries to answer the following question: What type of support should be given to an automobile driver when it is determined, via some method to monitor the driver's behavior and the traffic environment, that the driver's intent may not be appropriate to a traffic condition? With a medium fidelity, moving-base driving simulator, three conditions were compared: (a) Warning type support in which an auditory warning is given to the driver to enhance his/her situation recognition, (b) action type support in which an autonomous safety control action is executed to avoid an accident, and (c) the baseline condition in which no driver support is given. Results were as follows: (1) Either type of driver support was effective in accident prevention. (2) Acceptance of driver support functions varied context dependently. (3) Participants accepted a system-initiated automation invocation as long as no automation surprises were possible to occur.

The inverse problem related to nonlinear dynamical systems has received considerable attention as a basic problem concerning the construction of oscillating systems. Recently, F. Gonzaléz-Gascon, F. Moreno-Insertis, and E. Rodriguez-Camino presented an open problem on the synthesis of a two-dimensional dynamical system. We present a complete solution to the above-mentioned problem. We synthesize a structurally stable dynamical system having prescribed points and simple closed curves of class C4 as its singular points and closed orbits respectively. As to the problem above, we clarify a topological constraint which is necessary for the above-mentioned dynamical system to be synthesize. In addition, an example of a dynamical system with three closed orbits is given.

New communication systems via chaotic modulations are experimentally, demonstrated. They contain the wellknown chaotic circuits as its basic elements--Chua's circuits and canonial Chua's circuits. The following advantage is found in our laboratory experiments: (a) Transmitted signals have broad spectra. (b) Secure communications are possible in the sense that the better parameter matching is required in order to recover the signal. (c) The circuit structure of our communication system is most simple at this stage. (d) The communication systems are easily built at a small outlay.