Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations (Cambridge Texts in Applied Mathematics, Series Number 11)

By Providing An Introduction To Nonlinear Differential Equations, Dr Glendinning Aims To Equip The Student With The Mathematical Know-how Needed To Appreciate Stability Theory And Bifurcations. His Approach Is Readable And Covers Material Both Old And New To Undergraduate Courses. Included Are Treatments Of The Poincaré-bendixson Theorem, The Hopf Bifurcation And Chaotic Systems. The Unique Treatment That Is Found In This Book Will Prove To Be An Essential Guide To Stability And Chaos. Paul Glendinning. Includes Bibliographical References (p. 382-385) And Index. This book examines qualitative methods for nonlinear differential equations, bifurcation theory and chaos in terms suitable for advanced undergraduate and first-year postgraduate students in mathematics and physics. Starting from the idea of phase space, the structure of solutions near hyperbolic stationary points and periodic orbits is investigated. Then, after a brief discussion of perturbation methods and nonlinear oscillators, the theory of nonhyperbolic stationary points, bifurcations and chaos is described.The author's informal style and unified, coherent approach will enable students to investigate examples for themselves as they encounter nonlinear differential equations throughout the sciences.

By providing an introduction to nonlinear differential equations, Dr. Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems.