# American Institute of Mathematical Sciences

November  2019, 24(11): 5803-5830. doi: 10.3934/dcdsb.2019107

## Almost periodic dynamical behaviors of the hematopoiesis model with mixed discontinuous harvesting terms

 1 School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui 241000, China 2 Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain 3 Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain

* Corresponding author: Juan J. Nieto

Received  July 2018 Revised  December 2018 Published  June 2019

Discontinuous system is playing an increasingly important role in terms of both theory and applications. This paper presents a hematopoiesis model with mixed discontinuous harvesting terms. By using differential inclusions theory, the non-smooth analysis theory with Lyapunov-like approach, some new sufficient criteria are given to ascertain the existence, uniqueness and globally exponential stability of the bounded positive almost periodic solutions for the addressed model. Some previously known results are extended and complemented. Moreover, simulation results of two topical numerical examples are also delineated to demonstrate the effectiveness of the established theoretical results.

Citation: Fanchao Kong, Juan J. Nieto. Almost periodic dynamical behaviors of the hematopoiesis model with mixed discontinuous harvesting terms. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 5803-5830. doi: 10.3934/dcdsb.2019107
##### References:

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##### References:
Discontinuous harvesting term for system (5.1)
Time-domain behavior of the state variables $x_1$ and $x_2$ for system (5.1) with random initial conditions
Phase plane behavior of the state variables $x_1$ and $x_2$ for system (5.1)
Three-dimensional trajectory of state variables $x_1$ and $x_2$ for system (5.1)
Discontinuous harvesting term for system (5.2)
Time-domain behavior of the state variables $x_1$ and $x_2$ for system (5.2) with random initial conditions
Phase plane behavior of the state variables $x_1$ and $x_2$ for system (5.2)
Three-dimensional trajectory of state variables $x_1$ and $x_2$ for system (5.2)
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