Differential equation models and chaos

Author: Wang Shuhuo
Publisher:
Publish Date: 1999-02-01
Features: This book introduces the fundamental theory of differential equations. Classification of equilibrium points of planar linear systems, existence and uniqueness theorem of solutions to differential equations, concepts of dynamical systems, linearization methods, stability and Liapunov direct method, stable manifold theorem, center manifold method, topological equivalence of systems, Hartman-Grobman theorem, non-hyperbolic equilibrium points in the plane, Hamiltonian systems and gradient systems, elementary catastrophe theory of gradient systems, periodic orbits, limit cycles and boundary line cycles, Poincaré maps, Poincaré-Bendixson theorem on the plane, Liénard systems, Bendixson criterion, Poincaré sphere and behavior at infinity, global phase portraits and boundary line structures, structural stability, saddle-node bifurcation, Hopf topological equivalence, Hartman-Grobman theorem, non-hyperbolic equilibrium points in the plane, Hamiltonian systems and gradient systems, elementary catastrophe theory of gradient systems, periodic orbits, limit cycles and boundary line cycles, Poincaré maps, Poincaré-Bendixson theorem on the plane, Liénard systems