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Dynamics analysis of Mackey-Glass model with two variable delays

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

Special Issues: Applications of delay differential equations in biology

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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Keywords Mackey-Glass model; delay; global attractivity; stability

Citation: Yanxiang Tan. Dynamics analysis of Mackey-Glass model with two variable delays. Mathematical Biosciences and Engineering, 2020, 17(5): 4513-4526. doi: 10.3934/mbe.2020249


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