
Mathematical Biosciences and Engineering, 2020, 17(5): 45134526. doi: 10.3934/mbe.2020249
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Dynamics analysis of MackeyGlass 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
Received: , Accepted: , Published:
Special Issues: Applications of delay differential equations in biology
References
1. H. Hu, X. Yuan, L. Huang, C. Huang, Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks, Math. Biosci. Eng., 16 (2019), 57295749.
2. C. Qian, Y. Hu, Novel stability criteria on nonlinear densitydependent mortality Nicholson's blowflies systems in asymptotically almost periodic environments, J. Inequal. Appl., 2020 (2020), 13.
3. C. Huang, H. Zhang, L. Huang, Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear densitydependent mortality term, Commun. Pure Appl. Anal., 18 (2019), 33373349.
4. Y. Tan, C. Huang, B. Sun, T. Wang, Dynamics of a class of delayed reactiondiffusion systems with Neumann boundary condition, J. Math. Anal. Appl., 458 (2018), 11151130.
5. C. Huang, X. Long, L. Huang, S. Fu, Stability of almost periodic Nicholson's blowflies model involving patch structure and mortality terms, Canad. Math. Bull., 63 (2020), 405422.
6. C. Huang, H. Zhang, J. Cao, H. Hu, Stability and Hopf bifurcation of a delayed preypredator model with disease in the predator, Internat. J. Bifur. Chaos Appl., 29 (2019), 1950091.
7. X. Long, S. Gong, New results on stability of Nicholson's blowflies equation with multiple pairs of timevarying delays, Appl. Math. Lett., 100 (2020), 106027.
8. C. Huang, S. Wen, M. Li, F. Wen, X. Yang, An empirical evaluation of the influential nodes for stock market network: Chinese a shares case, Financ. Res. Lett., (2020), 101517.
9. X. Yang, S. Wen, Z. Liu, C. Li, Dynamic properties of foreign exchange complex network, Mathematics, 7 (2019), 832.
10. C. Huang, H. Yang, J. Cao, Weighted pseudo almost periodicity of multiproportional delayed shunting inhibitory cellular neural networks with D operator, Discrete Contin. Dyn. Syst. Ser. S, 2020.
11. C. Huang, X. Yang, J. Cao, Stability analysis of Nicholson's blowflies equation with two different delays, Math. Comput. Simulation, 171 (2020), 201206.
12. M. Iswarya, R. Raja, G. Rajchakit, J. Cao, J. Alzabut, C, Huang, Existence, uniqueness and exponential stability of periodic solution for discretetime delayed BAM neural networks based on coincidence degree theory and graph theoretic method, Mathematics, 7 (2019), 1055.
13. C. Huang, Z. Yang, T. Yi, X. Zou, On the basins of attraction for a class of delay differential equations with nonmonotone bistable nonlinearities, J. Differential Equations, 256 (2014), 2101 2114.
14. C. Huang, J. Cao, F. Wen, X. Yang, Stability analysis of SIR model with distributed delay on complex networks, PLoS One, 11 (2016), e0158813.
15. M. Mackey, L. Glass, Oscillation and chaos in physiological control systems, Science, 197 (1977), 287289.
16. C. Huang, X. Long, J. Cao, Stability of antiperiodic recurrent neural networks with multiproportional delays, Math. Meth. Appl. Sci., 43 (2020), 60936102.
17. L. Berezansky, E. Braverman, MackeyGlass equation with variable coefficients, Appl. Math. Comput., 51 (2006), 116.
18. L. Berezansky, E. Braverman, L. Idels, MackeyGlass model of hematopoiesis with nonmonotone feedback: Stability, oscillation and control, Appl. Math. Comput., 219 (2013), 62686283.
19. W. Wang, Global exponential stability for the MackeyGlass model of respiratory dynamics with a control term, Math. Meth. Appl. Sci., 39 (2016), 606613.
20. L. Berezansky, E. Braverman, A note on stability of MackeyGlass equations with two delays, J. Math. Anal. Appl., 450 (2017), 12081228.
21. C. Huang, J. Wang, L. Huang, New results on asymptotically almost periodicity of delayed Nicholsontype system involving patch structure, Electron. J. Differ. Equ., 2020 (2020), 117.
22. J. Alzabut, Y. Bolat, T. Abdeljawad, Almost periodic dynamics of a discrete Nicholson's blowflies model involving a linear harvesting term, Adv. Differ. Equ., 2012 (2012), 158.
23. S. Saker, J. Alzabut, Periodic solutions, global attractivity and oscillation of an impulsive delay hostmacroparasite model, Math. Comput. Model, 45 (2007), 531543.
24. S. Saker, J. Alzabut, On the impulsive delay hematopoiesis model with periodic coefficients, Rocky Mountain J. Math., 39 (2009), 16571688.
25. J. Alzabut, J. Nieto, G. Stamov, Existence and exponential stability of positive almost periodic solutions s for a model of hematopoiesis, Bound. Value Probl., (2009), 127510.
26. J. Alzabut, Almost periodic solutions for an impulsive delay Nicholson's blowflies model, J. Comput. Appl. Math., 234 (2010), 233239.
27. Y. Xu, Q. Cao, X. Guo, Stability on a patch structure Nicholson's blowflies systeminvolving distinctive delays, Appl. Math. Lett., 105 (2020), 106340.
28. C. Huang, Y. Qiao, L. Huang, R. Agarwal, Dynamical behaviors of a foodchain model with stage structure and time delays, Adv. Difference Equ., 2018 (2018), 186.
29. L. Duan, X. Fang, C. Huang, Global exponential convergence in a delayed almost periodic Nicholson's blowflies model with discontinuous harvesting, Math. Meth. Appl.Sci., 41 (2018), 19541965.
30. H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Springer New York, 2011.
31. H. A. ElMorshedy, A. RuizHerrera, Global convergence to equilibria in nonmonotone delay differential equations, Proc. Amer. Math. Soc., 147 (2019), 20952105.
32. I. Győri, F. Hartung, N. A. Mohamady, Permanence in a class of delay differential equations with mixed monotonicity, Electron. J. Qual. Theory Differ. Equ., 53 (2018), 121.
33. L. Berezansky, E. Braverman, L. Idels, The MackeyGlass model of respiratory dynamics: Review and new results, Nonlinear Anal., 75 (2012), 60346052.
34. L. Berezansky, E. Braverman, L. Idels, MackeyGlass model of hematopoiesis with monotone feedback revisited, Appl. Math. Comput., 219 (2013), 48924907.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)