| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1994: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥600,000 (Direct Cost: ¥600,000)
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| Research Abstract |
In this subject, we intended to clarify the concept of the self-organization in nonlinear electric circuits. For this purpose, we have tried to find the conditions to excite the 'chaos' , and elucidate the physical meaning of chaos as well as 'order' like the periodic phenomena and the synchronization. The main results of this study are as follows.
(1) We consider the 3rd order oscillators, which consist of five elements, i.e., a nonlinear active element, three linear positive capacitors and inductors in all, and a linear resistor. We clarified the relations between the transition of the stability of the equiliburium points and the occurrence of chaos, and obtained the necessary conditions for chaos. To apply these ideas to the oscillators with other nonlinear characteristics or the higher order is the subject for a future study.
(2) It is found that the essential behavior of an oscllator changes from non-excitation (no current) to the self-excited oscillation (A.C current) and the equilibrium point (D.C.current) , and that the chaos may occure as a kind of the special self-excited oscillation in a narrow parameter space. It is important to unify the physical meaning of these various phenomena using the concept of the 'averaged potential' which we proposed formerly.
(3) The synchronization of two identical relaxation oscillator is also studied. It is found that one of the syncronization becomes unstable as the nonlinearity increases. It is essential to clarify this phenomenon in order to understand the behavior of a circuit with many nonlinear elements.
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