神經(jīng)網(wǎng)絡、經(jīng)濟學和物理中的混沌復制（英文版）（Replication of Chaos in Neural Networks, Economics and Physic）
定 價：98 元
- 作者：Marat Akhmet， Mehmet Onur Fen 著
- 出版時間：2015/10/1
- ISBN：9787040431025
- 出 版 社：高等教育出版社
- 中圖法分類：O415.5
- 頁碼：457
- 紙張：膠版紙
- 版次：1
- 開本：16開
本書是講述諸如：電纜、柱體、棒條體、板材等薄的變形體的數(shù)學近似理論。由于非線性變形體動力學有著廣泛的應用，比如soft webs 及 rod-reinforced soft structures理論可用于DNA及活組織的生物動力學，且尚有一些解決的理論難題，本書的主要目的激發(fā)在該領域的更多的研究。本書可用于物理學、應用數(shù)學和生物物理學等專業(yè)研究生教材或相關研究人員的參考書。 Nonlinear Deformable-body Dynamics mainly consists in a mathematical treatise of approximate theories for thin deformable bodies,including cables, beams, rods, webs, membranes, plates, and shells. The intent of the bookis to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structurescan be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics.
1 Introduction
1.1 Synchronization of Chaotic Systems
1.2 Control of Chaos
1.3 Neural Networks and Chaos
1.4 Extension of Chaos
1.5 Ordering Chaos
1.6 Self-organization of Chaos
1.7 Morphogenesis of Chaos
1.8 Chaos and Cellular Automata
1.9 Synergetics and Chaos
1.10 Mathematics in Chaos Theory
1.11 Chaos Theory and Real World
1.12 Organization of the Book
References
2 Repfication of Continuous Chaos About Equilibria
2.1 Introduction
2.2 Preliminaries
2.3 Chaotic Sets of Functions
2.3.1 Devaney Set of Functions
2.3.2 Li-Yorke Set of Functions
2.4 Hyperbolic Set of Functions
2.5 Replication of Devaney's Chaos
2.6 Extension of Li-Yorke Chaos
2.7 Morphogenesis of Chaos
2.8 Period-Doubling Cascade
2.9 Control by Replication
2.10 Miscellany
2.10.1 Intermittency
2.10.2 Shilnikov Orbits
2.10.3 Morphogenesis of the Double-Scroll Chua's Attractor
2.10.4 Quasiperiodicity in Chaos
2.10.5 Replicators with Nonnegative Eigenvalues
2.11 Notes
References
3 Chaos Extension in Hyperbolic Systems
3.1 Introduction
3.2 Preliminaries
3.3 Extension of Chaos
3.4 Simulations
3.5 Notes
References
4 Entrainment by Chaos
4.1 Introduction
4.2 Preliminaries
4.3 Sensitivity
4.4 Unstable Periodic Solutions
4.5 Main Result
4.6 Examples
4.7 Miscellany
4.7.1 Chaotic Tori
4.7.2 Entrainment in Chua's Oscillators
4.7.3 Controlling Chaos
4.7.4 Entrainment and Synchronization
4.8 The Regular Motion Near the Limit Cycle
4.9 Notes
References
5 Chaotifieation of Impulsive Systems
5.1 Introduction
5.2 Preliminaries
5.3 Chaotic Dynamics
5.4 An Example
5.5 Notes
References
6 Chaos Generation in Continuous/Discrete-Time Models
6.1 Devaney's Chaos of a Relay System
6.1.1 Introduction and Preliminaries
6.1.2 The Chaos
6.1.3 The Chaos on the Attractor
6.1.4 The Period-Doubling Cascade and Intermittency: An Example
6.2 Li-Yorke Chaos in Systems with Impacts
6.2.1 Introduction and Preliminaries
6.2.2 Main Results
6.3 Li-Yorke Chaos in the System with Relay
6.3.1 Introduction and Preliminaries
6.3.2 The Li-Yorke Chaos
6.4 Dynamical Synthesis of Quasi-Minimal Sets
6.4.1 Introduction
6.4.2 Main Result
6.4.3 A Simulation Result
6.4.4 Appendix
6.5 Hyperbolic Sets of Impact Systems
6.6 Chaos and Shadowing
6.6.1 Introduction and Preliminaries
6.6.2 The Devaney's Chaos
6.6.3 Shadowing Property
6.6.4 Simulations
6.7 Chaos in the Forced Duffing Equation
6.7.1 Introduction and Preliminaries
6.7.2 The Chaos Emergence
6.7.3 Controlling Results
6.7.4 Morphogenesis and the Logistic Map
6.7.5 Miscellany
6.8 Notes
References
7 Economic Models with Exogenous Continuous/Discrete Shocks
7.1 Chaos in Economic Models with Equilibria
7.1.1 Introduction
7.1.2 Modeling the Exogenous Shock
7.1.3 Mathematical Investigation of System (7.1.5)
7.1.4 Chaos in a Kaldor-Kalecki Model
7.2 Chaotic Business Cycles
7.2.1 Introduction
7.2.2 The Input-Output Mechanism and Applications
7.2.3 Economic Models: The Base Systems
7.2.4 Chaos in a Stellar of Economical Models
7.2.5 Kaldor-Kalecki Model with Time Delay
7.2.6 Chaos Extension Versus Synchronization
7.3 The Global Unpredictability, Self-organization and Synergetics
7.4 Notes
References
8 Chaos by Neural Networks
8.1 SICNNs with Chaotic External Inputs
8.1.1 Introduction
8.1.2 Preliminaries
8.1.3 Chaotic Dynamics
8.1.4 Examples
8.2 Attraction of Chaos by Retarded SICNNs
8.2.1 Introduction
8.2.2 Preliminaries
8.2.3 Li-Yorke Chaos
8.2.4 An Example
8.2.5 Synchronization of Chaos
8.3 Impulsive SICNNs with Chaotic Postsynaptic Currents
8.3.1 Introduction
8.3.2 Preliminaries
8.3.3 The Existence of Chaos
8.3.4 Examples
8.4 Cyclic/Toroidal Chaos in Hopfield Neural Networks
8.4.1 Introduction
8.4.2 Entrainment by Chaos in HNNs
8.4.3 Control of Cyclic/Toroidal Chaos in Neural Networks
8.5 Notes
References
9 The Prevalence of Weather Unpredictability
9.1 Introduction
9.2 Coupling Mechanism for Unpredictability
9.3 Extension of Lorenz Unpredictability
9.4 Period-Doubling Cascade
9.5 Cyclic Chaos in Lorenz Systems
9.6 Intermittency in the Weather Dynamics
9.7 Self-Organization and Synergetics
9.8 The Mathematical Background
9.8.1 Bounded Positively Invariant RegiOn
9.8.2 Unpredictability Analysis
9.8.3 Unstable Cycles and Unpredictability
9.9 Notes
References
10 Spatiotemporal Chaos in Glow Discharge-Semiconductor Systems
10.1 Introduction
10.2 Preliminaries
10.2.1 Description of the GDS Model
10.2.2 The Model in Dimensionless Form
10.3 Chaotically Coupled GDS Systems
10.4 The Chaos in the Drive GDS System
10.5 Notes
References
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