导语

  

内容提要

  

    本书在国外是大学生物学专业本科生教材，全书取材得当，在阐明稳定性、分歧理论、分形以及混饨等现代动力学基本理论的同时，避免了过于复杂枯燥的数学陈述。书中实例多数选自生物化学、神经物理学、心病学和生态学等领域。书中对每一概念地有清晰明了的解释，并已有大量实例和生动准确的图表，因而使得全书非常浅显易懂。
    读者对象：生物学、物理学及其它非数学专业高年级本科生、研究生和科研人员。

SERIES PREFACE
ABOUT THE AUTHORS
PREFACE
1  FINITE-DIFFERENCE EQUATIONS
    1.1  A Mythical Field
    1.2  The Linear Finite-Difference Equation
    1.3  Methods of Iteration
    1.4  Nonlinear Finite-Difference Equations
    1.5  Steady States and Their Stability
    1.6  Cycles and Their Stability
    1.7  Chaos
    1.8  Quasiperiodicity
  1 Chaos in Periodically Stimulated Heart Cells,
    Sources and Notes
    Exercises
    Computer Projects
2  BOOLEAN NETWORKS AND CELLULAR AUTOMATA
    2.1  Elements and Networks
    2.2  Boolean Variables, Functions, and Networks
    2 A Lambda Bacteriophage Model
  3 Locomotion in Salamander,a
    2.3  Boolean Functions and Biochemistry
    2.4  Random Boolean Networks
    2.5  Cellular Automata
  4 Spiral Waves in Chemistry and aiology
    2.6  Advanced Topic: Evolution and Computation
    Sources and Notes
    Exercises
    Computer Projects
3  SELF-SIMILARITY AND FRACTAL GEOMETRY
    3.1  Describing a Tree
    3.2  Fractals
    3.3  Dimension
  5 The Box-Counting Dimension,
    3.4  Statistical Self-Similarity
  6 Self-Similarity in Time,
    3.5  Fractals and Dynamics
  7 Random Walks and Levy Walks
  8 Fractal Growth,
    Sources and Notes
    Exercises
    Computer Projects
4  ONE-DIMENSIONAL DIFFERENTIAL EQUATIONS
    4.1  Basic Definitions
    4.2  Growth and Decay
  9 Traffic on the Internet
  10 Open Time Histograms in Patch Clamp Experiments"
  11 Gompertz Growth of Tumors,
    4.3  Multiple Fixed Points
    4.4  Geometrical Analysis of One-Dimensional Nonlinear Ordinary Differential Equations
    4.5  Algebraic Analysis of Fixed Points
    4.6  Differential Equations versus Finite-Difference Equations
    4.7  Differential Equations with Inputs
  12 Heart Rate Response to Sinusoid Inputs
    4.8  Advanced Topic: Time Delays and Chaos
  13 Nicholson's Blowflies,
    Sources and Notes
    Exercises
    Computer Projects
5  TWO-DIMENSIONAL DIFFERENTIAL EQUATIONS
    5.1  The Harmonic Oscillator
    5.2  Solutions, Trajectories, and Flows
    5.3  The Two-Dimensional Linear Ordinary Differential Equation
    5.4  Coupled First-Order Linear Equations
  14 Metastasis of Malignant Tumors,
    5.5  The Phase Plane
    5.6  Local Stability Analysis of Two-Dimensional, Nonlinear Differential Equations
    5.7  Limit Cycles and the van der Pol Oscillator
    5.8  Finding Solutions to Nonlinear Differential Equations
  15 Action Potentials in Nerve Celis
    5.9  Advanced Topic: Dynamics in Three or More Dimensions
    5.10  Advanced Topic: Poincar6 Index Theorem
    Sources and Notes
    Exercises
    Computer Projects
6  TIME-SERIES ANALYSIS
    6.1  Starting with Data
    6.2  Dynamics, Measurements, and Noise
  16 Fluctuations in Marine Populations,
    6.3  The Mean and Standard Deviation
    6.4  Linear Correlations
    6.5  Power Spectrum Analysis
  17 Daily Oscillations in Zooplankton
    6.6  Nonlinear Dynamics and Data Analysis
  18 Reconstructing Nerve Cell Dynamics,
    6.7  Characterizing Chaos
  19 Predicting the Next Ice Age,
    6.8  Detecting Chaos and Nonlinearity
    6.9  Algorithms and Answers
    Sources and Notes
    Exercises
    Computer Projects
APPENDIX A A MULTI-FUNCTIONAL APPENDIX
  A.1  The Straight Line
  A.2  The Quadratic Function
  A.3  The Cubic and Higher-Order Polynomials
  A.4  The Exponential Function
  A.5  Sigmoidal Functions
  A.6  The Sine and Cosine Functions
  A.7  The Gaussian (or "Normal") Distribution
  A.8  The Ellipse
  A.9  The Hyperbola
  Exercises
APPENDIX B  A NOTE ON COMPUTER NOTATION
SOLUTIONS TO SELECTED EXERCISES
BIBLIOGRAPHY
INDEX