Chaotic Behavior in a Switching Delay Circuit

Matsuo, Akihito; Asahara, Hiroyuki; Kousaka, Takuji

doi:10.1587/transfun.e95.a.1329

Cited by 3 publications

(5 citation statements)

References 14 publications

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“…Figure 11 shows the two-parameter bifurcation diagram in the x r -T plane. Note that a similar bifurcation diagram is shown in Refs [22] and [23]; however, no detailed discussion of the circuit with ideal switching is given in that study. In the two-parameter bifurcation diagram, we show, for the sake of simplicity, that bifurcation sets in until the period-6 solution and 6-piece chaotic attractor.…”

Section: Case-dmentioning

confidence: 85%

“…In Refs [26][27][28][29][30], we proposed a simple IEC with nonideal switching and investigated the circuit characteristics. Moreover, we analyzed bifurcation phenomena of chaotic attractors in an IEC with nonideal switching in Refs [22][23][24]. However, the above papers contain little discussion of the ideal case, and no reports exist yet of the detailed bifurcation structure of chaotic attractors in an IEC with ideal switching.…”

Section: Introductionmentioning

confidence: 99%

“…However, few studies, except for Refs and , have investigated bifurcation phenomena of chaotic attractors with the inclusion of border‐collision bifurcation. To address this shortfall, we began analyzing bifurcation phenomena of the chaotic attractor in Refs . Although a detailed analysis is reported in Refs , it considers only a very special situation in which an IEC is driven by nonideal switching.…”

Section: Introductionmentioning

confidence: 99%

“…To address this shortfall, we began analyzing bifurcation phenomena of the chaotic attractor in Refs . Although a detailed analysis is reported in Refs , it considers only a very special situation in which an IEC is driven by nonideal switching. Note that high‐frequency switching ripples and switching delays, which occur because of floating capacitance or a time lag in the response to the switching signal, are typical examples of nonideal switching .…”

Section: Introductionmentioning

confidence: 99%

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Complete bifurcation analysis of a chaotic attractor in an electric circuit with piecewise‐smooth characteristics

Kousaka

Asahara

2014

IEEJ Transactions Elec Engng

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We investigate the bifurcation phenomena of chaotic attractors observed in electric circuits with piecewise‐smooth characteristics. First, we present a circuit model whose switching action depends on its own state and on the clock interval. Next, we explain the behavior of the waveform. Following this, we sample the waveform at every clock period to define the return map, which is vital for a detailed understanding of the circuit dynamics. Finally, bifurcation phenomena of chaotic attractors are classified into four cases with a focus on the invariant interval. In particular, we discuss the characteristics of each bifurcation phenomenon, and then clarify the bifurcation structure of the chaotic attractor. Moreover, some of the numerical results are verified experimentally. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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Section: Case-dmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Complete bifurcation analysis of a chaotic attractor in an electric circuit with piecewise‐smooth characteristics

Kousaka

Asahara

2014

IEEJ Transactions Elec Engng

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“…[19][20][21]. Thus, we previously proposed a one-dimensional composite dynamical system that simulates switching in a DC/DC converter in [22][23][24][25][26][27][28] and analyzed the effects of nonideal switching on a system from both the theoretical and the experimental perspective. The results showed that a new solution trajectory occurs due to the effects of nonideal switching, which affects the qualitative properties of the system.…”

Section: Introductionmentioning

confidence: 99%

Basic Properties of Two‐Dimensional Composite Dynamical System with Spike Noise

Tanaka

Asahara

Aihara

et al. 2015

Elect Comm in Japan

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SUMMARYBifurcation 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. C⃝ 2015 Wiley Periodicals, Inc. Electron Comm Jpn, 98(6): 26-35, 2015; Published online in Wiley Online Library (wileyonlinelibrary.com).

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