Paul Glendenning.
Stability, Instability and Chaos: an introduction to the theory of nonlinear differential equations.
CUP. 1994
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.