Bifurcation theory and applications - Ma, Tian (World Scientific, 2005)
Includes bibliographical references and index
Introduction to steady state bifurcation theory -- Introduction to dynamic bifurcation -- Reduction procedures and stability -- Steady state bifurcations -- Dynamic bifurcation theory: Finite dimensional case -- Dynamic bifurcation theory: Infinite dimensional case -- Bifurcations for nonlinear elliptic equations -- Reaction-diffusion equations -- Pattern formation and wave equations -- Fluid dynamics
This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. With this new notio
Keywords: MATHEMATICS / Differential Equations / General; Bifurcation theory; Differential equations, Nonlinear / Numerical solutions; Differential equations, Nonlinear -- Numerical solutions; Verzweigung -- Mathematik