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Dynamics analysis of Mackey-Glass model with two variable delays.

Yan Xiang Tan1

  • 1School of Mathematics and Statistics, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China.

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Summary

This study analyzes the non-autonomous Mackey-Glass model with two variable delays. New criteria ensure the stability of equilibrium points, improving existing research on this complex dynamical system.

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Area of Science:

  • Mathematical modeling
  • Dynamical systems theory
  • Differential equations

Background:

  • The dynamics of the non-autonomous Mackey-Glass model with two variable delays remain underexplored, representing an open problem.
  • Existing research lacks comprehensive documentation for this specific model configuration.

Purpose of the Study:

  • To investigate the attractivity of non-oscillating solutions around the positive equilibrium point.
  • To establish the global asymptotic stability of the trivial equilibrium point for the model.

Main Methods:

  • Development of two delay-independent criteria.
  • Application of the fluctuation lemma.
  • Utilization of differential inequality techniques.

Main Results:

  • Established criteria for the attractivity of non-oscillating solutions.
  • Proved the global asymptotic stability of the trivial equilibrium point.
  • Demonstrated improvement and complementarity to existing published results.

Conclusions:

  • The developed criteria provide a robust framework for analyzing the stability of the non-autonomous Mackey-Glass model with two variable delays.
  • Numerical simulations confirm the effectiveness and correctness of the established theoretical results.