MAT 604E - Differential Equations II

Course Objectives

1 To understand behavior sof the solution of linear and nonlinear differential equation systems near the fixed points
2 To understand the stability of the systems
3 To learn the fundamental and important theorems for dynamical systems
4 To learn the bifurcation theory

Course Description

Autonomous dynamical systems, existence and uniqueness, Lyapunov functions, Stabilty,potential functon and bifurcations for 1D autonomous systems, Linear autonomous systems and Lyapunov functions. Nonlinear autonomous systems, local analysis of fixed points,nonlinear centers, conservative systems, reversible systems, Index theory. Limit cycles, Dulac’s criterion, definition of orbital stability, The Poincare –Bendixson Theorem, Linard systems,Hopf bifurcation.