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Periodic functions related to the Gompertz difference equation.

Tom Cuchta1, Nick Wintz2

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This study explores the periodicity of functions within the Gompertz difference equation. We identified specific difference equations crucial for ensuring solution periodicity.

Keywords:
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Area of Science:

  • Mathematical analysis
  • Dynamical systems theory

Background:

  • The Gompertz difference equation is a mathematical model used in various fields, including population dynamics and economics.
  • Understanding the periodicity of solutions is essential for predicting long-term behavior and stability.

Purpose of the Study:

  • To investigate the conditions that lead to periodic solutions for functions associated with the Gompertz difference equation.
  • To derive novel difference equations that guarantee the periodicity of the Gompertz function's solutions.

Main Methods:

  • Analysis of difference equations.
  • Derivation of conditions for periodicity.
  • Mathematical modeling.

Main Results:

  • Established a set of necessary and sufficient conditions for the periodicity of solutions.
  • Derived specific difference equations that ensure periodic behavior.
  • Demonstrated the applicability of these conditions to the Gompertz difference equation.

Conclusions:

  • The derived difference equations provide a direct method for guaranteeing periodic solutions.
  • This research contributes to a deeper understanding of the qualitative behavior of the Gompertz difference equation.
  • Findings have implications for modeling systems exhibiting cyclical patterns.