Symmetry and Dynamical Analysis of a Discrete Time Model: The Higher Order Berverton-Holt Equation

TL;DR

This paper investigates the higher-order Beverton-Holt equation, deriving symmetries and solutions, analyzing periodicity and stability of equilibrium points to deepen understanding of its dynamical behavior.

Contribution

It introduces a symmetry-based approach to solving the higher-order Beverton-Holt equation and analyzes its stability and periodic solutions.

Findings

Derived nontrivial symmetries of the equation

Obtained explicit solutions for the model

Analyzed stability and periodicity of equilibrium points

Abstract

In this paper, we study the higher-order Beverton-Holt equation. We derive nontrivial symmetries, and thereafter, solutions are obtained. For constant rate and carrying capacity, we study the periodic nature of the solution and analyze the stability of the equilibrium points have been analyzed.