スパイクノイズを有する2次元合成力学系の定性的性質

概要

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Bifurcation phenomena in the composite dynamical system are studied for understanding basic properties of the systems. Recently, it has been reported that the unavoidable non-ideal switching action, e.g., the spike noise or the time delay, occurs via the switching action and seriously affects a behavior of the orbit in the composite dynamical systems operating in high-frequency switching ranges. We have analyzed basic property of a simple 1-dimensional composite dynamical system with non-ideal switching action for essentially understanding dynamical effect of the non-ideal switching. In the engineering field, however, there are many two- or more dimensional systems. Of course, the non-ideal switching action can occur in two- or more dimensional systems. But, no paper analyzes effect of the non-ideal switching action in it. In this paper, we study basic property of the 2-dimensional composite dynamical system with spike noise. First, we explain a model of the 2-dimensional composite dynamical system. Next, behavior of the waveforms, in the system with ideal switching and the system with spike noise, is shown. Then, we sample the data of the waveforms via every period of the external force, and define the Poincaré map. Finally, using the Poincaré map, we derive the 2-parameter bifurcation diagrams, and discuss the basic properties of the system with spike noise.