Mathematical Theory of Uniformity and its Applications in Ecology and Chaos (SpringerBriefs in Mathematical Methods)

✍ Scribed by Chuanwen Luo, Chuncheng Wang

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 100
• Category: Library

✦ Synopsis

This book puts forward a new mathematical theory to study chaotic phenomenon. The uniform theory is established on the basis of two elementary concept of circle and externally tangent square in mathematics. The author studies the uniformity of a finite set of points distributed in space by uniform theory. This book also illustrates that uniform theory performs better than other indices such as entropy and Lyapunov exponent in chaos measurement by numerous examples.
This book develops a new mathematical tool for studying chaos so it will be appealing to students and researchers interested in theory of chaos. It also has potential applications in various fields such as Engineering, Forestry and Ecology.

✦ Table of Contents

Preface
Contents
1 Uniform Degree
1.1 Introduction
1.2 Uniform Degree
1.3 Contained Uniform Degree Theorem
1.4 Uniform Degree Theorem for n-dim Random Pattern
1.5 Uniform Degree and Entropy
1.6 Numerical Test for the Conjecture
1.7 Applications of Uniform Degree Theorems in Plant Pattern Type Test
1.8 Universality of Uniformity Measurement
References
2 An Interpretation of Chaos by Uniform Degree
2.1 Introduction
2.2 Instantaneous Chaometry and k-Step Chaometry
2.3 Instantaneous Chaometry and Uniform Degree
2.4 More Applications of k-Step Chaometry
2.5 Application of 250-Step Chaometry in Heart Rate Problem
2.6 K-Step Chaometry in Vibration Fault Detection
References
3 Simulations on k-Step Chaometry
3.1 Introduction
3.2 Lorenz System
3.3 Application of Instantaneous Chaometry
3.4 ICM for Large k
4 Applications of Uniform Degree in Forestry and Ecology
4.1 Ecological Pattern
4.2 Monopolized Disk and Uniform Degree
4.3 Applications of Uniform Degree—The Rule of sqrt2
4.3.1 Monopolized Disk and Uniform Degree
4.3.2 Diversity of Distance
References