J. M. T. Thompson

Heilbroner calls the first view that of the Distant Past - the immense span that begins with the Stone Age, moves through the great early civilizations of the Near East to the glory that was Greece and the grandeur that was Rome, and ends only with the advent of modern times in the eighteenth century. Heilbroner makes the bold assertion that through all this vast panorama a single phrase depicts humanity's expectations of life on earth: it will be like the past. As he asks, what reason was there for expecting anything else? Change comes with the second, much shorter period, from the 1700s to the mid 1950s. Heilbroner calls it Yesterday. Now three immense forces, unknown in the Distant Past, dominate the expectations of the West. One of these is science, with its promise of controlling nature. A second is the advent of a dynamic means of organizing production called capitalism. And a third is the appearance of the revolutionary idea that the people themselves were the master of their destinies. Together these three forces imbue Yesterday's view of the future with an idea utterly unknown in the Distant Past: the expectation that the future will be better than the present. The third view is that of Today. Heilbroner points out that our own view of the future is still linked to science, capitalism, and democracy. What is new is that these powerful forces no longer appear as unambiguous carriers of progress. We look to science with fears as well as hopes; capitalism on a global scale brings economic difficulties along with new horizons; the expression of mass political sentiments conjures up the nightmares of Yugoslavia and Africa as well as possibilities for a widening of democratic government.

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 mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.