MA4620 Theory of Dynamical Systems

This course provides an introduction to the theory of dynamical systems providing a basis for the analysis and design of systems in engineering and applied science. It includes the following topics: Second order linear systems; contraction mapping, existence and uniqueness of solutions; continuous dependence on initial conditions; comparison principle; Lyapunov stability theorems; LaSalle's theorem; linearization methods; nonautonomous systems; converse theorems; center manifold theorems; and stationary bifurcations of nonlinear systems.

Prerequisite

MA2121

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

Upon completion of this course, the student should be able to:

• Solve linear ordinary differential equations of 1st and 2nd orders.
• Understand the fundamental theory of dynamical systems including the necessary theorems.
• Understand Grönwall's inequality and basic comparison principles and apply them to derive the bounds of solutions.
• Understand the definition of stabilities, including Lyapunov stability, asymptotic
• Know stability, local and global stabilities, and know how to apply Lyapunov functions to prove the stability of dynamical systems.
• Understand the concept of bifurcations; analyze the stability of bifurcations of co-dimension one and two; understand the dynamical behavior of supercritical and subcritical Hopf bifurcations.
• Understand the concept of controllability; understand the concept of feedback stabilization. Be able to design feedback for linear control systems.