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Ordinary Differential Equations (by Miller, R.K. and Michel, A.N.; 2007) [Bookshelf]

This book offers a twist for dynamical systems stability both in a linear and nonlinear setup. The material is rigorously presented and organized in a self-contained, yet not-too-pedantic manner. Some of the topics covered include: initial value problem; proving solutions; oscillation theory; boundary value problems; classical Lyapunov methods; the existence of stable and unstable manifolds; stability of periodic solutions, the Poincare-Bendixson theorem for planar systems, and Andronov-Hopf bifurcations. The material is adequate for both mathematicians and engineers at the "advanced undergraduate or graduate level," as remarked by the authors.