This book provides an introduction to the analysis of chaos and chaos theory as it relates to agricultural science. With clear explanations of chaos theory and principles, the first part of the book offers some basic facts, the fundamental terminology, and the concepts of deterministic chaos.

The second part of this volume contains rich applications of the theory as applied to real agricultural systems. Applications include a wide area such as alternate bearing in tree crops, weed control and tillage, nonlinear vibrations in agricultural tractors, and piglet pricing analysis.

Readers will find useful tools for calculating the order, rules and theory behind complex phenomena observed in arable land.

Table of Contents

Preface. Chapter 1. Introduction. Science and reproducibility. Chaos. Studies of chaos on agricultural systems. Summary of the book. Chapter 2. Deterministic Chaos. Concepts of deterministic chaos. Deterministic dynamical system. May's deterministic chaos. Complexity produced by simplicity. Return map. Period doubling route to chaos. Bifurcation diagram. Feigenbaum number. Discrete dynamical systems. One-dimensional discrete system. Malthusian growth model. Logistic growth model. Self-similarity of the bifurcation structure. Other one-dimensional discrete dynamical systems. Two-dimensional discrete dynamical system. Competition between two species. Prey-predator relationship. Continuous dynamical systems. Chaos of Lorenz System. Lorenz equation. Lorenz attractor. Chaos of Duffing's Equation. Duffing's Equation. Ueda's Chaos Attractor. Chapter 3. Analysis of Chaotic Data. Chaos time-series analysis. Spectral analysis. Delay coordinate embedding. Correlation dimension. Deterministic nonlinear prediction. Reconstruction of dynamics. Concept of prediction. Practice of prediction. Response surface methodology. Return map. Hassell's analysis. RSM analysis. Chapter 4. Numerical Practice on Chaotic Population Dynamics in Plant Communities. Dynamics of a weed community. Life table of a weed community.


No. of pages:
© 2001
Elsevier Science
Print ISBN:
Electronic ISBN:

About the editor

K. Sakai

Affiliations and Expertise

Associate Professor, Tokyo University of Agriculture and Technology, 3-5-8 Saiwai-cho, Fuchu-shi, Tokyo 183, Japan