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Basic Properties of Two‐Dimensional Composite Dynamical System with Spike Noise
Author(s) -
TANAKA DAIKI,
ASAHARA HIROYUKI,
AIHARA KAZUYUKI,
KOUSAKA TAKUJI
Publication year - 2015
Publication title -
electronics and communications in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 13
eISSN - 1942-9541
pISSN - 1942-9533
DOI - 10.1002/ecj.11659
Subject(s) - dynamical systems theory , noise (video) , bifurcation , spike (software development) , trajectory , spike train , waveform , dynamical system (definition) , field (mathematics) , statistical physics , ideal (ethics) , control theory (sociology) , computer science , mathematics , physics , nonlinear system , artificial intelligence , telecommunications , pure mathematics , radar , software engineering , control (management) , quantum mechanics , astronomy , image (mathematics) , philosophy , epistemology
SUMMARY Bifurcation phenomena in a composite dynamic system are studied in order to understand the basic properties of systems. Recently, it has been reported that unavoidable non‐ideal switching, e.g., spike noise or a time delay, occurs due to switching and seriously affects the behavior of the trajectory in a composite dynamical system operating in high‐frequency switching ranges. We have analyzed the basic properties of a simple one‐dimensional composite dynamical system with nonideal switching in order to understand the essence of the dynamical effects of nonideal switching. In the engineering field, there are many two‐ or more dimensional systems. Naturally, nonideal switching can occur in two‐ or more dimensional systems. However, no paper analyzes the effect of nonideal switching in such systems. In this paper, we study the basic properties of a two‐dimensional composite dynamical system with spike noise. First, we describe a model of a two‐dimensional composite dynamical system. Next, the behavior of the waveforms in a system with ideal switching and a system with spike noise is shown. Then, we sample the data of the waveforms in every period for the external force and define a Poincaré map. Finally, using the Poincaré map, we derive two‐parameter bifurcation diagrams and discuss the basic properties of a system with spike noise.