problemset4 - 2.050J\/12.006J\/18.353J Nonlinear Dynamics I Chaos Fall 2012 Problem Set 4 Due at 12:01 pm on Friday October 5th in the b ox provided No

# problemset4 - 2.050J/12.006J/18.353J Nonlinear Dynamics I...

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2.050J/12.006J/18.353J Nonlinear Dynamics I: Chaos, Fall 2012 Problem Set 4 Due at 12:01 pm on Friday, October 5th, in the box provided. No late psets are accepted. If you collaborated with other students in the class, list their names on the title sheet. The work that you submit must be your own. Main concepts: Three bifurcations in 1D dynamical systems (saddle-node, transcritical, and pitchfork). Reading: Strogatz Ch. 3. Problem 1: Bifurcations of 1D dynamical systems. Normal forms. For each of the following problems, sketch all the qualitatively different vector fields that occur as r is varied. Find at which x and for which critical values of the parameter r the bifurcation occurs. Which bifurcation is it (saddle-node, transcritical, supercritical pitchfork, or subcritical pitchfork)? Finally, sketch or plot in MATLAB the bifurcation diagram of fixed points x versus r , and mark the stable branches as solid lines, while the unstable branches as dashed lines. (Note: for some of the cases it is simpler to plot the bifurcation in MATLAB).

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• Fall '12
• LyubovChumakova
• Sets, Bifurcation, Bifurcation theory, 1D dynamical systems