Q13E
Question
Redo Problem 12 with F = 0.31. What kind of behavior does the solution exhibit?
Step-by-Step Solution
Verified Answer
By using the software, the Poincare maps are plotted and it shows chaotic behavior.
1Step 1: Sketch the Poincare map
Here the equation of (7) is:
\({\bf{x''(t) + bx' - x(t) + }}{{\bf{x}}^{\bf{3}}}{\bf{ = Fsin\gamma t}}\)
Put the given values when b = 0.3, \({\bf{\gamma }}\)= 1.2, and F=0.31
2Step 2: Sketch
Draw the graph using the given information.
Thus, the Poincare maps are plotted and it shows chaotic behavior.
Other exercises in this chapter
Q11E
To show that the limit set for the Poincare map \({{\bf{x}}_{\bf{n}}}{\bf{ = x(2\pi n),}}{{\bf{v}}_{\bf{n}}}{\bf{ = x'(2\pi n)}}\) where x(t) is a solution
View solution Q12E
Using a numerical scheme such as Runge–Kutta or a software package, calculate the Poincare map for equation (7) when b = 0.3, \({\bf{\gamma }}\)= 1.2, and
View solution Q14E
Redo Problem 12 with F = 0.65. What kind of behavior does the solution exhibit?
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Find a general solution\({\bf{x}}\left( {\bf{t}} \right){\bf{, y}}\left( {\bf{t}} \right)\)for the given system.\(\begin{array}{c}{\bf{x' + y'' + y
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