What do you think?
Rate this book
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.
935 pages, Kindle Edition
First published January 1, 1994
In the twenty years since this book first appeared, the ideas and techniques of nonlinear dynamics and chaos have found application in such exciting new fields as systems biology, evolutionary game theory, and sociophysics. To give you a taste of these recent developments, I’ve added about twenty substantial new exercises that I hope will entice you to learn more.
Throughout this chapter we have used graphical and analytical methods to analyze first-order systems. Every budding dynamicist should master a third tool: numerical methods.That is, you are allowed, indeed encouraged, to use a computer! You can never (well seldom) rigorously prove anything with numerical methods, and since proofs are what mathematics is all about, some mathematicians scorn numerical methods. Now, Strogatz is a mathematician. He knows what rigor is and employs it when it's the best way to an answer. But proofs in nonlinear dynamics are difficult, numerical methods are comparatively easy, and he uses both.
Throughout this chapter we have used graphical and analytical methods to analyze first-order systems. Every budding dynamicist should master a third tool: numerical methods.That is, you are allowed, indeed encouraged, to use a computer! You can never (well seldom) rigorously prove anything with numerical methods, and since proofs are what mathematics is all about, some mathematicians scorn numerical methods. Now, Strogatz is a mathematician. He knows what rigor is and employs it when it's the best way to an answer. But proofs in nonlinear dynamics are difficult, numerical methods are comparatively easy, and he uses both.