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