Theory and methods of nonlinear systems

Author: Han Mao'an
Publisher:
Publish Date: 2004-03-01
Features: This book primarily elaborates on the qualitative theory and bifurcation methods of nonlinear dynamical systems defined by ordinary differential equations, providing readers with fundamental knowledge and methods to open this door. The content includes the properties of planar linear systems, the hyperbolicity and stability of singular points in nonlinear systems, the classification of non-hyperbolic equilibrium points, the index theory, the center manifold theorem, periodic solutions and global bifurcations of periodic differential equations, stability and existence criteria for limit cycles, focus quantity and Hopf bifurcations, Poincaré bifurcations, subharmonic and homoclinic bifurcations, the averaging method, relaxation oscillations, the Lorenz system, bifurcations and chaos in the Duffing equation, the Melnikov method, and time series analysis methods, among others. This book is suitable for postgraduate students in science and engineering disciplines of higher education institutions and relevant scientific research workers.