Iterative Systems of Difference Equations

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SUMMARY

The discussion focuses on solving iterative systems of difference equations, specifically the equation x_{n+1} = x_{n}^{2}. Participants explore the concept of fixed points, identifying that at a fixed point, xn = xn+1. The fixed points for the given equation are determined to be x = 0 and x = 1. The conversation emphasizes understanding attracting and repelling fixed points in the context of iterative systems.

PREREQUISITES
  • Understanding of iterative systems in mathematics
  • Familiarity with difference equations
  • Knowledge of fixed points and their significance
  • Concepts of attracting and repelling fixed points
NEXT STEPS
  • Study the stability of fixed points in iterative systems
  • Learn about the graphical interpretation of difference equations
  • Explore advanced topics in nonlinear dynamics
  • Investigate applications of difference equations in real-world scenarios
USEFUL FOR

Mathematicians, students studying dynamical systems, and anyone interested in the analysis of iterative processes and fixed point theory.

kathrynag
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If one were to solve an iterative system, how would they do so. I'm studying them, and am wondering how to find fixed points?
For example, say I have [tex]x_{n+1}[/tex]=[tex]x_{n}^{2}[/tex] and was looking at fixed points how would I do so. I'm studying fixed points and attracting and repelling.
 
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Hi kathrynag! :smile:

(try using the X2 tag just above the Reply box :wink:)

At a fixed point, you can put xn = xn+1 …

in your example, the fixed points will be x = 0 or 1. :smile:
 

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