Find b & r for Periodic Trajectory of f(x) = r*x/(1+x)^b

In summary, the question is asking for values of b and r that will cause trajectories to be attracted to a periodic trajectory in the function f(x) = r*x/(1+x)^b. No proofs are necessary, just a numerical demonstration is needed.
  • #1
Ljilja
1
0
Hi all,
I am new to this forum.
My question is:
Find values of b and r for which trajectories are attracted to a periodic trajectory.
The function is:
f(x) = r*x/(1+x)^b

No proofs needed, just a numerical demonstration.


Thanks a lot,
Ljilja
 
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  • #2
Hiya Ljilja and welcome to the forums,

For future reference we have dedicated homework forums for such questions. In addition, according to the forum guidelines you are required to show some sort of effort in solving the problem yourself.

What are your thoughts?
 
  • #3
I also presume that the whole question hasn't been stated; ie. the word trajectory (to me) implies a differential equation [tex]\dot{x}=f(x)[/tex]
 

Related to Find b & r for Periodic Trajectory of f(x) = r*x/(1+x)^b

1. What is a periodic trajectory?

A periodic trajectory is a repeating pattern or path that a function follows over a certain period of time. In other words, it is a cyclical movement or behavior of a function.

2. How do you find the values of b and r for a periodic trajectory?

To find the values of b and r for a periodic trajectory of a function, you can use the method of least squares. This involves fitting a curve to the data points of the function and finding the best-fit values for b and r that minimize the sum of the squared differences between the data points and the curve.

3. What is the significance of b and r in a periodic trajectory?

The values of b and r in a periodic trajectory represent the shape and amplitude of the function's periodic behavior. B determines the rate at which the function approaches its maximum value, while r determines the amplitude or height of the function's peaks.

4. Can b and r change over time in a periodic trajectory?

Yes, b and r can change over time in a periodic trajectory. This can happen if the function is affected by external factors such as changing environmental conditions or if there are underlying changes in the system that the function is modeling.

5. How does the shape of the function change with different values of b and r in a periodic trajectory?

The shape of the function in a periodic trajectory can vary greatly with different values of b and r. Changing the value of b can alter the rate at which the function reaches its maximum value, while changing the value of r can change the amplitude or height of the function's peaks. Therefore, different combinations of b and r can result in a wide range of shapes and patterns for the function's periodic behavior.

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