Bulletin of the Japan Society for Industrial and Applied Mathematics

Online ISSN : 2432-1982

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Volume 7, Issue 4

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[title in Japanese]

Article type: Cover
1997 Volume 7 Issue 4 Pages Cover1-
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_Cover1

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[title in Japanese]

Article type: Index
1997 Volume 7 Issue 4 Pages Toc1-
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_Toc1

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[title in Japanese]

Article type: Index
1997 Volume 7 Issue 4 Pages Toc2-
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_Toc2

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On the review

Hiroshi Niki

Article type: Article
1997 Volume 7 Issue 4 Pages 255-
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_255

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[title in Japanese]

Article type: Appendix
1997 Volume 7 Issue 4 Pages 256-257
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_256

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Dynamical Systems : Recent Developments in Applied Mathematics

Hiroshi Kokubu

Article type: Article
1997 Volume 7 Issue 4 Pages 258-259
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_258

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Embedding Theory of Dynamical Systems and Reconstructing Attractors from Data Time Series(<Special Topics>Dynamical Systems-Recent Developments in Applied Mathematics-)

Tohru Ikeguchi, Kazuyuki Aihara

Article type: Article
1997 Volume 7 Issue 4 Pages 260-270
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_260

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This paper reviews such embedding theorems of dynamical systems as Takens' embedding theory and the extended theory by Sauer et al. and practical methods to reconstruct possible attractors only from observed time series data. These are bases for time series analysis from the view point of nonlinear dynamical systems theory. The reconstruction method by filtered delay coordinates is also discussed.

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Bifurcation Diagram Reconstruction : Reconstructing a Parameterized Family of Dynamical Systems only from Time-Wave Forms-(<Special Topics>Dynamical Systems-Recent Developments in Applied Mathematics-)

Ryuji Tokunaga, Takashi Matsumoto, Isao Tokuda

Article type: Article
1997 Volume 7 Issue 4 Pages 271-282
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_271

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This paper reports a simple algorithm for reconstructing bifurcation diagrams only from time-wave forms of a parameterized family of dynamical systems, without knowing an explicit form of the dynamics and its dependence on the parameters. The algorithm consists of two steps. First, nonlinear predictors are sought using a particular class of nonlinear functions with a lot of model parameters. Second, significant parameters contributing the bifurcation are found by the principal component analysis. Using the parameterized family of nonlinear predictors, it is possible to obtain bifurcation diagram qualitatively similar to that of the original systems. The algorithm is tested against Henon equation and Rossler equation.

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Receht Progress of Lattice Dynamical Systems(<Special Topics>Dynamical Systems-Recent Developments in Applied Mathematics-)

Shui-Nee Chow, John Mallet-Paret, Yasumasa Nishiura (translation)

Article type: Article
1997 Volume 7 Issue 4 Pages 283-292
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_283

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We survey recent advances in the theory of lattice dynamical systems. Among the topics discussed are pattern formation and spatial chaos, bifurcation of patterns, and traveling waves and propagation failure. We also discuss a class of equilibria called mosaic solutions, which are composed of the elements +1, -1, and 0, placed at each lattice point. A stability criterion for such solutions is given. The spatial entropy h of the set of all such stable solutions is defined, and we study how this quantity varies with parameters. Systems are qualitatively distinguished according to whether h=0 (termed pattern formation) , or h>0 (termed spatial chaos).

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A Geometric Approach to Systems with Maltiple Time Scales(<Special Topics>Dynamical Systems-Recent Developments in Applied Mathematics-)

Christopher K. R. T. Jones, Kunimochi Sakamoto (translation)

Article type: Article
1997 Volume 7 Issue 4 Pages 293-302
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_293

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By employing the invariant manifold theory developed by Fenichel, singularly perturbed dynamical systems are analysed with a special emphasis on then as multiple time scale systems. Exposition of the theory is guided by an example, the celebrated Hodgkin-Huxley Equatrons. More specifically, a geometric approach is given to the construction of homoclinic orbits which represent travelling pulses on nerve axons. In this approach, Exchange Lemma, together with Fenichel-normal forms, plays the decisive role.

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Methods of Computer Simulation on Dynamical Systems(<Special Topics>Dynamical Systems-Recent Developments in Applied Mathematics-)

Hiroshi Kawakami, Tetsuya Yoshinaga, Tetsushi Ueta

Article type: Article
1997 Volume 7 Issue 4 Pages 303-311
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_303

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In dynamical systems, the geometrical approach with computer simulation technique is useful to investigate nonlinear phenomena, such as properties of invariant set, local and global bifurcations, generation of chaotic state, and so on. We present an introduction to methods for constructing computational algorithms on dynamical systems described by ordinary differential equations. Some effective algorithms derived from the geometric and numeric methods to determine bifurcation values are concretely summarized. Namely, we give elementary methods for obtaining parameter values of codimension-one and -two bifurcations of periodic solutions and appearance of separatrix loop in autonomous system. We also mention some of the most popular package programs developed to support the analysis of dynamical systems.

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George Boole : His life and Works

Masaya Yamaguti

Article type: Article
1997 Volume 7 Issue 4 Pages 312-315
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_312

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Report from Prof. De Micheli's Laboratory at Stan ford University(Overseas,Laboratories)

Shin-ichi Minato

Article type: Article
1997 Volume 7 Issue 4 Pages 316-318
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_316

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ECEI Group, Tohoku University(Domestic,Laboratories)

Kazuyoshi Mori

Article type: Article
1997 Volume 7 Issue 4 Pages 319-320
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_319

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Fourth SIAM Conference on Applications of Dynamical Systems(Conference Reports)

Kazuyuki Yagasaki

Article type: Article
1997 Volume 7 Issue 4 Pages 321-322
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_321

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International Conference on Navier-Stokes Equations, Theory and Numerical Methods(Conference Reports)

Naoyuki Ishimura

Article type: Article
1997 Volume 7 Issue 4 Pages 322-
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_322

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The Fourth International Conference on Methematical Methods for Curves and Surfaces(Conference Reports)

Fujiichi Yoshimoto

Article type: Article
1997 Volume 7 Issue 4 Pages 323-
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_323_1

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Asymptotics in Nonlinear Diffusive Systems(Conference Reports)

Eiji Yanagida

Article type: Article
1997 Volume 7 Issue 4 Pages 323-324
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_323_2

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Encyclopedia of Chaos

Shigehiro Ushiki

Article type: Article
1997 Volume 7 Issue 4 Pages 325-326
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_325

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Two Books on Dynamical Systmes

Shigeru Tanaka

Article type: Article
1997 Volume 7 Issue 4 Pages 326-327
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_326

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[title in Japanese]

Article type: Appendix
1997 Volume 7 Issue 4 Pages 328-329
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_328

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[title in Japanese]

Article type: Appendix
1997 Volume 7 Issue 4 Pages 330-331
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_330

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[title in Japanese]

Article type: Index
1997 Volume 7 Issue 4 Pages 332-333
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_332

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[title in Japanese]

Article type: Index
1997 Volume 7 Issue 4 Pages Toc3-
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_Toc3

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[title in Japanese]

Article type: Cover
1997 Volume 7 Issue 4 Pages Cover2-
Published: December 15, 1997
Released on J-STAGE: April 08, 2017

DOIhttps://doi.org/10.11540/bjsiam.7.4_Cover2

JOURNAL FREE ACCESS

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