10.1/2(AM)(d) DYNAMICAL SYSTEMS
UNIT I:
LINEAR SYSTEMS
Exponentials of operators, The fundamental theorem for linear systems, Stability theory.
(Chapter 1 of the text book 1)
UNIT II:
INTRODUCTION TO NONLINEAR SYSTEMS:
Fundamental theorem of Existence and uniqueness, Continuous dependence of solutions on initial conditions, Flow of a differential equation.
(Sections 2.1 to 2.5 of Chapter 2 of the text book 1)
UNIT III:
LOCAL THEORY
Linearization, Stability, Liapunov functions, Gradients.
(Sections 2.6 to 2.14 of the text book 1)
UNIT IV:
GLOBAL THEORY
Limit sets and Attractors, Periodic orbits, Limit cycles, Painare – Bendixson Theory in R2 applications.
(sections 3.1 to 3.7 of Chapter 3 of the text book 1)
Text Book:
[1] Lawrence Perko, Differential Equations and dynamical systems, Springer(2001)
Reference:
[1] Hirch M.W and Smale S. Dynamical systems, Aeas press(1974)
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