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 Forestry and Ecology.

Autorentext

Dr. Chuanwen Luo received his B.S. degree in Mathematics from Chongqing Normal University, Chongqing, China, in 1983, M.S in Mathematical Ecology and Ph.D. in Ecology from Northeast Forestry University, Harbin, Heilongjiang, China, in 1985 and 1988 respectively. Since 1989, Dr. Luo has been in the School of Forestry, Northeast Forestry University as Lecture, Associate Professor and Professor. Dr Luo focuses on the research of mathematical biology and nonlinear science, and has published 28 peer-reviewed research papers and 4 monographs in the area of mathematics and forestry. Dr Chuncheng Wang received his B.E. degree in Mathematics from Dalian University of Technology, Dalian, Liaoning, China, in 2004, and the Ph.D. degree in Mathematics from Harbin Institute of Technology, Harbin, Heilongjiang, in 2010. Since April 2010, Dr. Wang has been in the Department of Mathematics, Harbin institute of Technology as Lecture, AssociateProfessor and Professor. Dr. Wang focuses on the research of differential equations, dynamical systems and mathematical biology. His recent research interests include: stability and bifurcations on the equilibrium of various differential equations, such as delay differential equations, partial functional differential equations and neutral equations; mathematical model and its analysis in ecology and epidemiology. Dr. Wang has published 23 peer-reviewed research papers and 1 textbook for graduate students since 2008. He also served as a reviewer of several international journals, and section chair of 2015 ICIAM international conference.