Spring 2017 : Math 134 - Linear and Nonlinear Systems of Differential Equations

- Evaluation

- Useful Link

PPlane by John C. Polking, Department of Mathematics, Rice University

http://math.rice.edu/~dfield/dfpp.html

XPS by G. Bard Ermentrout, Department of Mathematics, University of Pittsburgh

http://www.math.pitt.edu/~bard/xpp/xpp.html

Matlab

- Phase portraits

http://educ.jmu.edu/~strawbem/Phase_how_to.pdf

- Phase portraits of a system of ODEs and Plotting Solutions

http://matlab.cheme.cmu.edu/2011/08/09/phase-portraits-of-a-system-of-odes/

(See the link below for 'ode45' function

https://www.mathworks.com/help/matlab/ref/ode45.html

)

- Software Shortcut

https://software.library.ucla.edu/vpn/index.html

Example.

Exercise 2.2.1. in our textbook.

Analyze the following equations graphically. Sketch the vector field on the real line, find all the fixed points, classify their stability, and sketch the graph of x(t) for different initial conditions.

Matlab Code 1(without normalization)

Matlab Code 2(with normalization)

PPlane(Dfield)