Fixed points are values of x when
the two sides of the iterated map are equal as n->∞. This means that fixed points are essentially the solution of the iterative equation.
Here we have:
xn+1=3xb/(xn+1)
(please check my interpretation of your equation)
To find fixed points, using the definition of fixed points, we have
xn+1=3xb/(xn+1)
since x=xn+1=xn
we reduce the equation to:
x=3x/(x+1)
transpose and solve
x(x+1)=3x
x(x-2)=0
x=0 or x=2.
You can check iterating the given equation, you will get eventually 2 with all non-zero starting values, and zero is obtained only when initial value of x equals zero.
Given an iterated map, ie. x_n+1 = 3* x_n / (x_n +1),
how do we find all of its fixed points?
2 answers
Sorry, messed up codes, the iterative equation should read:
xn+1=3xn/(xn+1)
xn+1=3xn/(xn+1)