TABLE OF CONTENTS This chapter is entirely dedicated to the study of the stability of solutions to certain systems of differential equations. In the first section we introduce and illustrate the main concepts referring to stability. The second one is concerned with several necessary and sufficient conditions for various types of stability in the particular case of first-order systems of linear differential equations. In the third section we present some sufficient conditions under which the asymptotic stability of the null solution of a first-order differential system is inherited by the null solution of a certain perturbed system, provided the perturbation is small enough. In the fourth section we prove several sufficient conditions for stability expressed by means of some functions decreasing along the trajectories, while in the fifth section we include several results regarding the stability of solutions of dissipative systems. In the sixth section we analyze the stability problem referring to automatic control systems, while the seventh section is dedicated to some considerations concerning instability and chaos. As each chapter of this book, this one also ends with an Exercises and Problems section.
In its usual meaning, stability is that property of a particular state of a given system of preserving the features of its evolution, as long as the perturbations of the initial data are sufficiently small. This meaning comes from Mechanics, where it describes that property of the equilibrium state of a conservative system of being insensitive la longue to any kind of...
