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Analytical Solution to a Third-Order Rational Difference Equation.

Alvaro H Salas S1, Gilder Cieza Altamirano2,3, Rafaél Artidoro Sandoval Núñez2

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Summary
This summary is machine-generated.

This study analytically solves a third-order rational difference equation, inspired by dynamical systems. The derived solution is more accurate than the linearized equation

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Area of Science:

  • Mathematics
  • Dynamical Systems
  • Difference Equations

Background:

  • Addresses open conjectures in rational dynamical systems.
  • Focuses on solving third-order rational difference equations.

Purpose of the Study:

  • To analytically solve a specific third-order rational difference equation.
  • To analyze and comment on Ladas' conjecture.
  • To compare the exact solution with the linearized equation's solution.

Main Methods:

  • Analytical solution of a third-order rational difference equation.
  • Comparison with the solution of the linearized counterpart.
  • Calculation of the solution's period.

Main Results:

  • An analytical solution for the third-order rational difference equation is obtained.
  • The solution to the linearized equation is shown to be generally inaccurate.
  • The period of the derived solution is calculated and illustrated with examples.

Conclusions:

  • The analytical method provides an accurate solution for the studied difference equation.
  • Linearized solutions are not universally reliable for such equations.
  • The employed methods are applicable to other rational difference equations.