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A new method to investigate almost periodic solutions for an Nicholson’s blowflies model with time-varying delays and a linear harvesting term

1 Guizhou Key Laboratory of Economics System Simulation Guizhou University of Finance and Economics, Guiyang 550004, PR China
2 School of Mathematics and Physics, University of South China Hengyang 421001, PR China
3 School of Mathematics and Statistics, Henan University of Science and Technology Luoyang 471023, PR China
4 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology, Changsha 410114, PR China
5 School of Mathematics and Statistics, Central South University Changsha 410083, PR China

Special Issues: Mathematical Modeling to Solve the Problems in Life Sciences

In this paper, a delayed Nicholson’s blowflies model with a linear harvesting term is investigated. By transforming the model into an equivalent integral equation, and applying a fixed point theorem inc ones, we establish a sufficient condition which ensure the existence of positive almost periodic solutions for the Nicholson’s blowflies model. The results of this paper are completely new and complement those of the previous studies. The approach is new.
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References

1. A.L. Nicholson, An outline of the dynamics of animal populations, Aust. J. Zool., 2 (1954), 9–65.

2. W.S. Gurney, S.P. Blythe and R.M. Nisbet, Nicholson's blowflies revisited, Nat., 287 (1980), 17–21.

3. M.R.S. Kulenovic, G. Ladas and Y.G. Sficas, Global attractivity in population dynamics, Comput. Math. Appl., 18 (1989), 925–928.

4. J.W.H. So and J.S. Yu, On the stability and uniform persistence of a discrete model of Nicholson's blowflies, J. Math. Anal. Appl., 193 (1995), 233–244.

5. X.H. Ding and W.X. Li, Stability and bifurcation of numerical discretization Nicholson's blowflies equation with delay, Discrete Dyn. Nat. Soc., 2006 (2006),19413.

6. S.H. Saker and B.G. Zhang, Oscillation in a discrete partial delay Nicholson's blowflies model,Math. Comput. Modelling, 36 (2002), 1021–1026.

7. J.W.LiandC.X.Du, ExistenceofpositiveperiodicsolutionsforageneralizedNicholson'sblowflies model, J. Comput. Appl. Math., 221 (2008), 226–233.

8. W.T. Li and Y.H. Fan, Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholson's blowflies model, J. Comput. Appl. Math., 201 (2007), 55–68.

9. B.G. Zhang and H.X. Xu, A note on the global attractivity of a discrete model of Nicholson's blowflies, Discrete Dyn. Nat. Soc., 3 (1999), 51–55.

10. J.J. Wei and Michael Y. Li, Hopf bifurcation analysis in a delayed Nicholson's blowflies equation,Nonlinear Anal., 60 (2005), 1351–1367.

11. S.H. Saker and S. Agarwal, Oscillation and global attractivity in a periodic Nicholson's blowflies model, Math. Comput. Modelling, 35 (2002), 719–731.

12. B.W. Liu, Global dynamic behaviors for a delayed Nicholson's blowflies model with a linear harvesting term, Electron. J. Qual. Theor. Diff. Equat., 45 (2013), 1–13.

13. J.O. Alzabut, Almost periodic solutions for an impulsive delay Nicholson's blowflies model, J. Comput. Appl. Math., 234 (2010), 233–239.

14. T. Faria, Global asymptotic behaviour for a Nicholson model with path structure and multiple delays, Nonlinear Anal., 74 (2011) 7033–7046.

15. L.V. Hien, Global asymptotic behaviour of positive solutions to a non-autonomous Nicholson's blowflies model with delays, J. Biol. Dyn., 8 (2014), 135–144.

16. P. Amster and A. Deboli, Existence of positive T-periodic solutions of a generalized Nicholson's blowflies model with a nonlinear harvesting term, Appl. Math. Lett., 25 (2012), 1203–1207.

17. C.J. Xu, M.X. Liao and Y.C. Pang, Existence and convergence dynamics of pseudo almost periodic solutions for Nicholson's blowflies model with time-varying delays and a harvesting term, Acta Appl. Math., 146 (2016), 95–112.

18. H. Zhou, Z.F. Zhou and Z.M. Qiao, Mean-square almost periodic solution for impulsive stochastic Nicholson's blowflies model with delays, Appl. Mathe. Comput., 219 (2013), 5943–5948.

19. C.J. Xu, P.L. Li and Y.C. Pang, Exponential stability of almost periodic solutions for memristor-based neural networks with distributed leakage delays, Neural Comput., 28 (2016), 2726–2756.

20. Z.J. Yao, Existence and exponential stability of the unique positive almost periodic solution for impulsive Nicholson's blowflies model with linear harvesting term, Appl. Math. Modelling, 39 (2015), 7124–7133.

21. L.G. Yao, Dynamics of Nicholson's blowflies models with a nonlinear density-dependent mortality,Appl. Math. Modelling, 64 (2018), 185–195.

22. L. Berezansky, E. Braverman and L. Idels, Nicholson's blowflies differential equations revised: Main results and open problem, Appl. Math. Modelling, 34 (2010), 1405–1417.

23. A.M. Fink, Almost Periodic Differential Equations(Lecture Notes in Mathematics), 1974th edition, Springer, Berlin, 1974.

24. C.Y. He, Almost Periodic Differential Equation, Higher Education Publishing House, Beijing, 1992.

25. F. Long, Positive almost periodic solution for a class of Nicholson's blowflies model with a linear harvesting term, Nonlinear Anal.: Real World Appl., 13 (2012), 686–693.

26. H.S. Ding and J.J. Nieto, A new approach for positive almost solutions to a class of Nicholson's blowflies model, J. Comput. Appl. Math., 253 (2013), 249–254.

27. X.A. Hao, M.Y. Zuo and L.S. Liu, Multiple positive solutions for a system of impulsive integral boundary value problems with sign-changing nonlinearities, Appl. Math. Lett., 82 (2018), 24–31.

28. Y.Z. Bai and X.Q. Mu, Global asymptotic stability of a generalized SIRS epidemic model with transfer from infectious to susceptible, J. Appl. Anal. Comput., 8 (2018), 402–412.

29. M.M. Li and J.R. Wang, Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations, Appl. Math. Comput., 324 (2018), 254–265.

30. X.K. Cao and J.R. Wang, Finite-time stability of a class of oscillating systems with two delays,Math. Meth. Appl. Sci., 41 (2018), 4943–4954.

31. X.X. Zheng, Y.D. Shang and X.M. Peng, Orbital stability of periodic traveling wave solutions to the generalized Zakharov equations, Acta Mathe. Scientia, 37B (2017), 998–1018.

32. X.H. Tang and S.T. Chen, Ground state solutions of Nehari-Pohožaev type for Kirchhoff-type problems with general potentials, Calc. Var. Partial Diff. Equat., 56 (2017), 1–25.

33. S.T. Chen and X.H. Tang, Improved results for Klein-Gordon-Maxwell systems with general nonlinearity, Discrete Contin. Dyn. Syst. A, 38 (2018), 2333–2348.

34. S.T. Chen and X.H. Tang, Geometrically distinct solutions for Klein-Gordon-Maxwell systems with super-linear nonlinearities, Appl. Math. Lett., 90 (2019), 188–193.

35. S.T. Chen and X.H. Tang, Ground state solutions of Schrödinger-Poisson systems with variable potential and convolution nonlinearity, J. Math. Anal. Appl., 473 (2019), 87–111.

36. L. Duan, L.H. Huang, Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term, Math. Meth. Appl. Sci., 38 (2015), 1178–1189.

37. J.O. Alzabut, Almost periodic solutions for an impulsive delay Nicholson's blowflies model, J. Comput. Appl. Math., 234 (2010), 233–239.

38. W. Wang, L. Wang and W. Chen, Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems, Nonlinear Anal.: Real World Appl., 12 (2011), 1938–1949.

39. W. Chen and B. Liu, Positive almost periodic solution for a class of Nicholson's blowflies model with multiple time-varying delays, J. Comput. Appl. Math., 235 (2011), 2090–2097.

40. Z. Huang, S. Mohamad, X. Wang, et al., Convergence analysis of general neural networks under almost periodic stimli, Int. J. Circ. Theor. Appl., 37 (2009), 723–750.

41. F.X. Lin, Exponential Dichotomies of Linear System, Anhui University Press, Hefei, 1999.

42. W.A. Coppel, Dichotomies in Stability Theory(Lecture Notes in Mathematics), 1978th edition, Springer, Berlin, 1978.

43. H.S. Ding and T.J. Xiao, Existence of positive almost automorphic solutions to nonlinear delay integral equations, Nonlinear Anal.: Theory, Meth. Appl., 70 (2009), 2216–2231.

44. F. Chérif, Pseudo almost periodic solution of Nicholson's blowflies model with mixed delays, Appl. Math. Modelling, 39 (2015), 5152–5163.

45. Z.J. Yao, Uniqueness and global exponential stability of almost periodic solution for Hematopoiesis model on time scales, J. Nonlinear Sci. Appl., 8 (2016), 142–152.

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