An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #"Book Review - " "Engineering Societies Library, New York"#1 "An attempt to make research tools concerning strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #"American Mathematical Monthly"#2

"This book is written with the reality of biology students and their apprehension about mathematics in mind. The applications of mathematical models to real biological problems are not contrived, as they are in a number of other texts. And the biology examples are taken from the current literature--a wonderful help to those who will be teaching with this book."--Jim Keener, University of Utah, author of "Principles of Applied Mathematics" and "Mathematical Physiology"

""Dynamic Models in Biology" is a new and significant contribution to the field. Very well written and clearly presented, it fulfills its goal of bringing dynamic models into the undergraduate biology curriculum. Indeed it puts biology first, and then seeks to show how biological phenomena can be explained in mathematical terms."--Martin Henry H. Stevens, Miami University

"This excellent book is a major contribution to the literature. Strong biologically and mathematically, well-organized, and engagingly written, it introduces the subject of dynamical models in biology in as coherent a way as I have seen anywhere. Few authors could approach this topic as authoritatively as do Ellner and Guckenheimer."--Simon Levin, Princeton University, author of "The Importance of Species" and "The Encyclopedia of Biodiversity"