Nonlinear dynamics in complex systems : theory and applications for the life-, neuro- and natural sciences
著者
書誌事項
Nonlinear dynamics in complex systems : theory and applications for the life-, neuro- and natural sciences
(Springer complexity)
Springer, c2013
大学図書館所蔵 全2件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. [229]-230) and index
内容説明・目次
内容説明
With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.
This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work.
"This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future."
"With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems."
"What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically."
(J.A.Scott Kelso, excerpts from the foreword)
目次
Part I Nonlinear Dynamical Systems.- Introduction.- One-dimensional Systems.- Two-Dimensional Systems.- Higher-Dimensional Systems and Chaos.- Discrete Maps and Iterations in Space.- Stochastic Systems.- Part II: Model Systems.- Haken-Kelso-Bunz (HKB) Model.- Self-organization and Synergetics.- Neuronal Models.- Part III: Mathematical Basics.- Mathematical Basics.- The Coupled HKB System.- Numerical Procedures and Computer Simulations.- Solutions.
「Nielsen BookData」 より