• May 9th, 2015

Nonlinear Dynamics

Paper, Order, or Assignment Requirements

 

 

2 questions. I will need complete answer for the two questions with the MATLAB code for each one.

 

Show all you work including any Matlab code. Points will be awarded for correct answers as well as your discussion and justification of results.

Problem 1: LIMIT CYCLES

Discuss the number and nature of limit cycles in the following system:

Use phase portraits, bifurcation diagram, and numerical integration as needed to justify your answer.

Describe key characteristics of any limit cycle you find such as slow fast dynamics. Discuss eigenvectors associated with the limit cycle.

Problem 2:      CHAOS

The following system exhibits chaotic behavior:

Using bifurcation diagram and numerical integration estimate the critical value of ratio A/B for which chaos emerges. Select w=10 and e=1.

Clearly demonstrate that critical value of ratio A/B results in chaotic behavior by explicitly showing that two very close trajectories grow apart as time progresses.

 

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