Dynamics analysis of Mackey-Glass model with two variable delays

Yanxiang Tan; Yanxiang Tan

doi:10.3934/mbe.2020249

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 4513-4526. doi: 10.3934/mbe.2020249

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Dynamics analysis of Mackey-Glass model with two variable delays

Yanxiang Tan ^,

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

Received: 30 April 2020 Accepted: 15 June 2020 Published: 24 June 2020

Dynamics of non-autonomous Mackey-Glass model have not been well documented yet in two variable delays case, which is proposed by Berezansky and Braverman as open problems. This manuscript considers attractivity of all non-oscillating solutions about the positive equilibrium point and the global asymptotical stability of the trivial equilibrium point. Two delay-independent criteria based on the fluctuation lemma and techniques of differential inequality are established. The obtained results improve and complement some published results. Meanwhile, computer simulations of two numerical examples are arranged to illustrate the correctness and effectiveness of the presented results.
- Mackey-Glass model,
- delay,
- global attractivity,
- stability
Citation: Yanxiang Tan. Dynamics analysis of Mackey-Glass model with two variable delays[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4513-4526. doi: 10.3934/mbe.2020249

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Abstract

Dynamics of non-autonomous Mackey-Glass model have not been well documented yet in two variable delays case, which is proposed by Berezansky and Braverman as open problems. This manuscript considers attractivity of all non-oscillating solutions about the positive equilibrium point and the global asymptotical stability of the trivial equilibrium point. Two delay-independent criteria based on the fluctuation lemma and techniques of differential inequality are established. The obtained results improve and complement some published results. Meanwhile, computer simulations of two numerical examples are arranged to illustrate the correctness and effectiveness of the presented results.

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