Nonlinear Systems [Paperback]

This book introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics.The text introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. Worked examples and problems are used to motivate and illustrate the general principles.The text introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. Worked examples and problems are used to motivate and illustrate the general principles.A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.1. Introduction; 2. Classification of bifurcations of equilibrium solutions; 3. Difference equations; 4. Some special topics; 5. Ordinary differential equations; 6. Second-order autonomous ordinary differential systems; 7. Forced oscillations; 8. Chaos; Bibliography; Index. This is a volume in the series Cambridge Texts in Applied mathematics. It is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as the parameter varies... Quarterly of Applied Mathematics ...can be used as an effective text to introduce the topics involved with nonlinear dynal3–