Dynamical Systems and Chaos - MATH3201


	Faculty: Faculty of Science
	School: School of Mathematics and Statistics
	Course Outline: http://www.maths.unsw.edu.au/
	Campus: Kensington Campus
	Career: Undergraduate
	Units of Credit: 6
	EFTSL: 0.12500 (more info)
	Indicative Contact Hours per Week: 4
	Enrolment Requirements:
	Prerequisite: 12 units of credit in Level 2 Mathematics courses including MATH2120 or MATH2130, and MATH2501 or MATH2601, or both MATH2019(DN) and MATH2089, or both MATH2069(CR) and MATH2099.
	Fee Band: 5 (more info)
	Further Information: See Class Timetable

Description

A dynamical system is any system whose state changes as a function of time. This course studies the regular and irregular behaviour of nonlinear dynamical systems, concentrating on ordinary differential equations (ODEs) and their solutions.

Topics from the theory of ODEs include: existence and uniqueness theorems; linear ODEs with constant and periodic coefficients and Floquet theory; linearization and stability analysis; perturbation methods; bifurcation theory; phase plane analysis for autonomous systems. The theory is illustrated with applications to physical, biological and ecological systems.

In addition, a selection from the dynamical concepts: Hamiltonian dynamics, resonant oscillations, chaotic systems, Lyapunov exponents, Poincare maps, homoclinic tangles.