Basics of nonlinearities in mathematical sciences

'This book is primarily an attempt to familiarize the reader with nonlinear systems, in particular qualitative characteristics in a variety of systems amenable to mathematization. Differential equations form the bulk of the book, while the basics of nonlinearities are presented through theorems and problems, aiming to bring out the essence of some aspects of nonlinearities in the emerging discipline of mathematical science. Qualitative studies that reflect the evolution of nonlinearities have not thus far been approached in this way.'

This book is primarily an attempt to familiarize the reader with nonlinear systems, particularly qualitative characteristics, in a variety of systems amenable to mathematization. Differential equations form the bulk of the book, while the basics of nonlinearities are presented through theorems and problems, aiming to bring out the essence of some aspects of nonlinearities in the emerging discipline of mathematical science. Qualitative studies that reflect the evolution of nonlinearities have not thus far been approached in this way.

The uniqueness of the book lies in coupling historical perspectives with the latest trends in nonlinearities. Appendices are intended for inquisitive users of the book for further developments. This book will be of interest to students of mathematics at the postgraduate and undergraduate level, while those involved in the disciplines of physics, chemistry, biology, ecology, technology and economics should also find the work intriguing.

Preamble -- Motivation -- Recapturing linear ordinary differential equations -- Linear systems : qualitative behaviour -- Stability studies -- Study of equilibria : another approach -- Non-linear vis a vis linear systems -- Stability aspects : Liapunov's direct method -- Manifolds : introduction and applications in nonlinearity studies -- Periodicity : orbits, limit cycles, Poincare map -- Bifurcations : a prelude -- Catastrophes : a prelude -- Theorizing, further, bifurcations and catastrophes -- Dynamical systems -- Epilogue.