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<p>This paper investigates biological patterns using difference equation systems to analyze the complex dynamics of biological systems. The study focuses on analyzing the stability of certain systems, simplifying them around equilibrium points, and determining solution properties such as boundedness and persistence. Through the calculation of the Jacobian matrix, stability around the equilibrium point is analyzed, and conditions for local stability are identified. The boundedness and persistence of solutions are proven under specific conditions, with a subset of the system ensuring solutions remain within a defined range. Additionally, attraction and global stability of the equilibrium point are analyzed, demonstrating its local and global attractiveness under specified conditions. Numerical simulations are conducted to study how initial conditions and various parameters affect the stability of biological patterns. This work highlights the importance of using mathematical models to understand and analyze biological patterns.</p>

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Stability analysis of biological rhythms using three-dimensional systems of difference equations with squared terms

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Hashem Althagafi,
  • Ahmed Ghezal

摘要

This paper investigates biological patterns using difference equation systems to analyze the complex dynamics of biological systems. The study focuses on analyzing the stability of certain systems, simplifying them around equilibrium points, and determining solution properties such as boundedness and persistence. Through the calculation of the Jacobian matrix, stability around the equilibrium point is analyzed, and conditions for local stability are identified. The boundedness and persistence of solutions are proven under specific conditions, with a subset of the system ensuring solutions remain within a defined range. Additionally, attraction and global stability of the equilibrium point are analyzed, demonstrating its local and global attractiveness under specified conditions. Numerical simulations are conducted to study how initial conditions and various parameters affect the stability of biological patterns. This work highlights the importance of using mathematical models to understand and analyze biological patterns.