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## An Introduction to Nonlinear Systems Chaos

by: Dr. Filomena Hegmann

46

0

2

# An Introduction to Nonlinear Systems Chaos APPM 3010

Marketplace > University of Colorado at Boulder > Applied Math > APPM 3010 > An Introduction to Nonlinear Systems Chaos
Dr. Filomena Hegmann

GPA 3.76

Staff

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COURSE
PROF.
Staff
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Class Notes
PAGES
2
WORDS
KARMA
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## Popular in Applied Math

This 2 page Class Notes was uploaded by Dr. Filomena Hegmann on Thursday October 29, 2015. The Class Notes belongs to APPM 3010 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 46 views. For similar materials see /class/231876/appm-3010-university-of-colorado-at-boulder in Applied Math at University of Colorado at Boulder.

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Date Created: 10/29/15
APPM 3010 Review for Exam 1 1 Fundamentals 0 Given an ODE7 possibly a higher order scalar equation andor a nonautonomous equation7 be able to put it in the form of a rst order7 autonomous system 0 Given a multi step map7 be able to write it as a system of 1 step maps Be able to provide examples of various types of dynamical sys tems eg maps and ODES7 linear and nonlinear7 autonomous and nonautonomous7 high order scalar equations and systems of equations 2 Well posedness Be able to state the existence and uniqueness theorem for ODEs Be able to state the theorems given in class regarding continuity in initial conditions and parameters Be able to explain why these ideas are important in modeling physical systems Know the di erence between local and global existence 0 Given an explicit fx7 if7 A be able to determine a range of initial conditions where the initial value problem lVP x fX7t7 A is locally well posed Be able to determine a range of initial condi tions where the corresponding solutions exist for all time Be able to give examples of lVPs where uniqueness fails Be able to give examples of lVPs whose solutions blow up in nite time 3 Flows on the real line 0 Given i f either explicitly or as a graph7 be able to determine the equilibria of the ow and their stability by graphing 0 Be able to determine the curvature of solutions by computing i f mi 0 Given a phase portrait be able to give an example of an lVP i f that is consistent With that phase portrait 0 Give a collection of solutions t be able to give an example of an lVP i f that is consistent With those solutions 0 Be able to determine the stability of an equilibrium point by lin earization From linearization be able to determine the asymp totic rate of decay to or growth from the equilibrium point 4 Bifurcations 0 Given a rst order equation With a parameter be able to determine When if at all a bifurcation occurs 0 Know the basic characteristics of the saddle node transcritical and pitchfork bifurcations including their bifurcation diagrams 0 Be able to determine if one of these bifurcations occurs in a given system that is not in the canonical form

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