Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Volume 3 , Issue 2
Showing 1-13 articles out of 13 articles from the selected issue
Special Section on Synchronization in Nonlinear Science and Engineering
  • Tohru Ikeguchi, Isao Tokuda
    Type: FOREWORD
    2012 Volume 3 Issue 2 Pages 112
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    Synchronization is a ubiquitous phenomenon of coupled nonlinear oscillators, commonly found in physics, engineering, biology, and other diverse disciplines. It has a long research history back to Christiaan Huygens, who discovered synchronized motion of two pendulum clocks in 1673. It is very easy to observe synchronization in our daily life: e.g., metronomes, candle fires, pet-bottle oscillators, saltwater oscillators, and so on(See, for example, experimental movies at http://www.youtube.com/user/IkeguchiLab?feature=watch). For the last few decades, significant development has been made from both theories and experiments on synchronization of coupled limit cycle oscillators as well as coupled chaotic oscillators. Applications have been also developed to communication technologies, controlling techniques, and data analysis. Combined with the idea from complex network theory, neuroscience, and systems biology, the research speed of synchronization has been even accelerated. This Special Section of NOLTA is primarily dedicated to the recent advanced development of basics and applications of synchronization in science and engineering. A number of qualified works is included, ranging from experimental study on synchronization of Huygens' system, analog circuits, and singing voice to applied study of synchronization in communication networks. One invited paper is devoted to comprehensive reviews on generalized synchronization of chaotic oscillators. On behalf of the editorial committee of the special section, the guest editors would like to express their sincere thanks to all the authors for their excellent contributions. In particular, they are grateful to Prof. Dr. Ulrich Parlitz for contributing his distinguished review article. They would also like to thank the reviewers and the members of the guest editorial committee, especially Prof. Hiroo Sekiya of Chiba University and the editorial staffs of the NOLTA journal, for their supports on publishing this Special Section.
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  • Ulrich Parlitz
    Type: Invited Paper
    2012 Volume 3 Issue 2 Pages 113-127
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    Different cases of generalized synchronization are discussed with emphasis on methods for detecting them from time series. In particular, we shall focus on synchronization resulting in complex (non-smooth and/or non-invertible) functions or relations between drive and response.
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  • J. Peña-Ramírez, R.H.B. Fey, H. Nijmeijer
    Type: Paper
    Subject area: Nonlinear Problems
    2012 Volume 3 Issue 2 Pages 128-142
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    In this experimental study, phase synchronization is studied in pairs of nonlinear oscillators coupled through a movable support. In particular, the dynamics of two discontinuous mass-spring-damper oscillators and the dynamics of the classical Huygens' pendulum clocks are considered. In both systems the individual oscillators are self-sustained. It is shown that in both cases, the oscillators exhibit in-phase and anti-phase synchronization. All experiments are executed on a new experimental setup consisting of two controllable mass-spring-damper oscillators coupled through an elastically supported rigid bar. The results suggest, that the synchronized motion observed by Christiaan Huygens around 1650 in a pair of pendulum clocks mounted on a flexible support, in many cases can also be observed when the pendulum clocks are replaced by other self-sustained nonlinear oscillators.
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  • Kazutaka Kanno, Atsushi Uchida
    Type: Paper
    Subject area: Nonlinear Problems
    2012 Volume 3 Issue 2 Pages 143-154
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    We investigate generalized synchronization and complexity in unidirectionally coupled Rössler systems and Mackey-Glass systems with time-delayed feedback. The generalized synchronization is measured by using two identical response systems which are driven by a common drive system. To measure the complexity, KS entropy and KY dimension are calculated quantitatively from the Lyapunov spectrum by using the linearized equations. The response systems show generalized synchronization for large coupling strengths. The entropy and dimensionality decrease as the coupling strength is increased. The minimum value of entropy is obtained at the condition of generalized synchronization, whose value corresponds to the entropy for the solitary drive system, even though the temporal waveforms of the drive and response systems are significantly different. The maximum entropy is achieved outside the region where generalized synchronization is achieved, whose value almost corresponds to the sum of those of the two solitary drive and response systems. It is found that the coupling effect changes the entropy within these two values. The dimensionality decreases monotonically even within the region of generalized synchronization.
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  • Masahiko Tateno, Atsushi Uchida
    Type: Paper
    Subject area: Nonlinear Problems
    2012 Volume 3 Issue 2 Pages 155-164
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    We experimentally and numerically investigate chaos generation in a Mackey-Glass electronic circuit with two time-delayed feedback loops. We observe different dynamic behaviors when the two delay times are varied. The ratio of the two time delays is crucial for enhancing or suppressing the chaotic dynamics. We also investigate chaos synchronization in unidirectionally coupled Mackey-Glass electronic circuits with two time delays. Experimental and numerical results confirm that chaos synchronization can be achieved even when there are two time-delayed feedback loops. High-quality chaos synchronization can be achieved with high coupling strengths and parameter-matching conditions between the two electronic circuits.
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  • Daniele Linaro, Marco Righero, Mario Biey, Marco Storace
    Type: Paper
    Subject area: Nonlinear Problems
    2012 Volume 3 Issue 2 Pages 165-179
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    This paper uses synchronization as a tool for further validating a circuit (HR-PWL circuit) recently proposed in the literature and based on a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model. The accuracy of the single neuron hardware implementation has been already validated through bifurcation analysis tools. Here, the synchronization behavior of networks formed by HR neurons is simulated and compared to that of companion networks of PWL neurons, with the purpose of validating the HR-PWL circuit also from a collective behavior point of view. In the considered cases, the neurons are connected either by linear diffusive or by nonlinear sigmoidal coupling, with different topologies. The analysis is based on the Master Stability Function approach and is verified by extensive numerical time-domain simulations. The synchronization properties of the PWL neuron networks turn out to be qualitatively very similar to those of the companion HR networks, confirming the validity of the proposed hardware-implemented neuron.
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  • Kenji Matsuzaka, Takashi Tohara, Kazuki Nakada, Takashi Morie
    Type: Paper
    Subject area: Nonlinear Problems
    2012 Volume 3 Issue 2 Pages 180-190
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    Analog CMOS circuit implementation of a system of pulse-coupled phase oscillators is proposed. A CMOS circuit that achieves the dynamics of pulse-coupled oscillators has been designed and fabricated using a 0.25-µm CMOS technology. The proposed oscillator circuits with continuous-time operation interact with each other via a pulse at each firing time. Update of the oscillator state is achieved by integrating the phase sensitivity function with the pulse width time span. The phase sensitivity function is generated by the combination of binary functions, while the function consists of three-values {-1,0,1}. Introducing a zero-value span in the function leads to fast synchronization and robustness to parameter fluctuation due to LSI device mismatches, which facilitates VLSI implementation. Using the fabricated CMOS circuit, we have observed not only in- and anti-phase but also out-of-phase synchronization.
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  • Ryota Aisu, Takehiko Horita
    Type: Paper
    Subject area: Nonlinear Problems
    2012 Volume 3 Issue 2 Pages 191-199
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    The response to a time periodic treatment of the immunotherapy in a stochastic model of tumor-immune interaction is numerically investigated. Due to the effect of synchronization among the intrinsic oscillation and the treatment, an enhanced extinction of the tumor cells is observed. It suggests that compared with the static treatment, by controlling the period of the treatment, the time periodic treatment could be an effective way of treatment leading to tumor extinction.
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  • Kosuke Sanada, Hiroo Sekiya, Nobuyoshi Komuro, Shiro Sakata
    Type: Paper
    Subject area: Nonlinear Problems
    2012 Volume 3 Issue 2 Pages 200-214
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    In IEEE 802.11 wireless multi-hop networks, each node works individually and their individual operations generate entire network dynamics. It is important to clarify the network dynamics in wireless multi-hop networks for designing and constructing multi-hop communication networks. This paper presents the network-dynamics investigations for three-hop string-topology wireless network in detail. From the investigations, a “backoff-stage synchronization” phenomenon, which is mutuality between hidden nodes, is found. The mechanism of the backoff-stage synchronization is expressed and the sufficient conditions for the synchronization occurrence are given. This phenomenon gives some impacts on the IEEE 802.11 multi-hop-network communications.
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  • Isao Tokuda, Akihiro Kuwahara
    Type: Paper
    Subject area: Nonlinear Problems
    2012 Volume 3 Issue 2 Pages 215-221
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    Synchronization plays an essential role in choir singing. Fundamental frequencies of the singing voices should satisfy a rational frequency relationship to produce harmony. The present study attempts to clarify basic properties of synchronization that may influence the chorus quality. As the key features of synchronization, frequency mismatch and timing mismatch were considered. Combining the synthesis technique of choir singing, which can precisely control the detailed frequency structure of the singing voice, with psychoacoustic experiment, criterions were obtained to roughly discriminate good choruses from bad ones. To examine the reliability of the psychoacoustic experiment, acoustic analysis of the singing voices in real chorus was further carried out.
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Regular Section
  • Masaki Igarashi, Masayuki Ikebe, Sohsuke Shimoyama, Junichi Motohisa
    Type: Paper
    Subject area: Nonlinear Image Processing
    2012 Volume 3 Issue 2 Pages 222-232
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    We propose a constant-time algorithm for a bilateral filter. Bilateral filter can be converted into the operation of three-dimensional (3D) convolution. By using recursive moving sum, we can reduce the number of calculations needed to construct a pseudo-Gaussian filter. Applying one-dimensional Gaussian filter to the 3D convolution, we achieved a constant-time bilateral filter. We used a 3-GHz CPU without SIMD instructions, or multi-thread operations. We confirmed our proposed bilateral filter to be processed in constant time. In practical conditions, high PSNR values over 40 dB are obtained.
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  • Masayuki Kimura, Takashi Hikihara
    Type: Paper
    Subject area: Nonlinear Waves
    2012 Volume 3 Issue 2 Pages 233-245
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    A macro-mechanical cantilever array is proposed for experimental investigation of intrinsic localized modes (ILMs). The array is designed to have tunable on-site potentials that can be adjusted individually. Thus, it is easy to realize an array, in which an ILM can be excited. In addition, impurities can be induced in and removed from the array. Several ILMs were successfully generated by an external sinusoidal excitation, and the generated ILMs were manipulated by adding an impurity to the cantilever array. The manipulation mechanism is discussed numerically on the basis of the structure of phase space. Coexisting ILMs, unstable manifolds, and the domains of attraction of a stable ILM are shown for an ILM manipulated by adding an impurity.
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  • Yuki Kawai, Tadashi Tsubone
    Type: Paper
    Subject area: Control of Chaos
    2012 Volume 3 Issue 2 Pages 246-256
    Published: 2012
    Released: April 01, 2012
    JOURNALS FREE ACCESS
    Stability transformation method has been proposed in order to detect the location of a unstable periodic orbit in a dynamical system which exhibits chaotic behavior. A chaos control approach based on the method has been also considered. The chaos control method can stabilize unknown steady states, however the control method uses l-times iterated Poincaré map corresponding to a periodic orbit of length l. Therefore there is a disadvantage related to robustness and more detailed discussion for realization of the control method is needed. In this paper, we propose a novel chaos control method based on stability transformation method for unstable periodic orbits. The method can stabilize unstable periodic orbits whose states are unknown. We show that our method has a much wider range of control parameters to guarantee stability than ones of a previous method and can be realized by a simple circuit implementation. Some examples are provided and the some theoretical results are confirmed by laboratory measurements.
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