This textbook is aimed at newcomers to nonlinear dynamics and
chaos, especially students taking a first course in the subject.
The presentation stresses analytical methods, concrete examples and
geometric intuition. The theory is developed systematically,
starting with first-order differential equations and their
bifurcations, followed by phase plane analysis, limit cycles and
their bifurcations, and culminating with the Lorenz equations,
chaos, iterated maps, period doubling, renormalization, fractals,
and strange attractors. A unique feature of the book is its
emphasis on applications. These include mechanical vibrations,
lasers, biological rhythms, superconducting circuits, insect
outbreaks, chemical oscillators, genetic control systems, chaotic
waterwheels, and even a technique for using chaos to send secret
messages. In each case, the scientific background is explained at
an elementary level and closely integrated with the mathematical
theory. Richly illustrated, and with many exercises and worked
examples, this book is ideal for an introductory course at the
juniorsenior or first-year graduate level. It is also ideal for
the scientist who has not had formal instruction in nonlinear
dynamics, but who now desires to begin informal study. The
prerequisites are multivariable calculus and introductory
physics.