Concept explainers
Interpretation:
For anoverdamped system forced by a square wave given by
Concept Introduction:
Poincare map is defined by
Answer to Problem 3E
Solution:
a)
b)
c) The limits of
d) The Poincare map
e) Using a cobweb picture,
Explanation of Solution
a)
The given system equations are
Multiply the complete equation by
Integrate it with respect to
But,
Divide the complete equation by
Rearrange it as:
Let
Hence, it is proved.
b)
Suppose that the system has a T-periodic solution. Then,
But
Rearrange it as
Hence, it is proved.
c)
Similarly,
These results are plausible. Since as
As
And the solution becomes
d)
Since,
In a general form, it can be written as
It is a straight line equation of the form
The plot of
e)
The cobweb plot of the given system at
Since
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Chapter 8 Solutions
Nonlinear Dynamics and Chaos
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage