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New result on the global attractivity of a delay differential neoclassical growth model

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Abstract

This paper is concerned with the effect of delay on the asymptotic behavior of a differential neoclassical growth model with multiple time-varying delays. By using the fluctuation lemma and some differential inequality technique, delay-dependent criteria are obtained for the global attractivity of the addressed system. Meanwhile, some numerical examples are given to illustrate the feasibility of the theoretical results.

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References

  1. Matsumoto, A., Szidarovszky, F.: Delay differential neoclassical growth model. J. Econ. Behav. Organ. 78, 272–289 (2011)

    Article  Google Scholar 

  2. Matsumoto, A., Szidarovszky, F.: Asymptotic behavior of a delay differential neoclassical growth model. Sustainability 5, 440–455 (2013)

    Article  Google Scholar 

  3. Berezansky, L., Braverman, E., Idels, L.: Nicholsons blowflies differential equations revisited: main results and open problems. Appl. Math. Model. 34, 1405–1417 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Liu, B.: Global exponential stability of positive periodic solutions for a delayed Nicholsons blowflies model. J. Math. Anal. Appl. 412, 212–221 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Xiong, W.: New results on positive pseudo-almost periodic solutions for a delayed Nicholsons blowflies model. Nonlinear Dyn. 85, 563–571 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, W., Wang, W.: Global exponential stability for a delay differential neoclassical growth model. Adv. Differ. Equ. 325, 1–9 (2014)

    MathSciNet  Google Scholar 

  7. Duan, L., Huang, C.: Existence and global attractivity of almost periodic solutions for a delayed differential neoclassical growth model. Math. Methods Appl. Sci. 40(3), 814–822 (2017)

  8. So, J.W., Yu, J.: Global attractivity and uniform persistence in Nicholsons blowflies. Differ. Equ. Dyn. Syst. 2(1), 11–18 (1994)

    MathSciNet  MATH  Google Scholar 

  9. Li, J.: Global attractivity in Nicholson’s blowflies. Appl. Math. JCU 11(4), 425–434 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dang, V.G., Lenbury, Y., Seidman, T.I.: Delay effect in models of population growth. J. Math. Anal. Appl. 305(305), 631–643 (2005)

    MathSciNet  MATH  Google Scholar 

  11. Dang, V.G., Lenbury, Y., Gaetano, A.D.: Delay model of glucose–insulin systems: global stability and oscillated solutions conditional on delays. J. Math. Anal. Appl. 343(2), 996–1006 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liz, E., Tkachenko, V., Trofimchuk, S.: A global stability criterion for scalar functional differential equations. SIAM J. Math. Anal. 35(3), 596–622 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Smith, H.L.: Monotone dynamical systems. An Introduction to the Theory of Competitive and Cooperative Systems (Mathematical Surveys and Monographs). In: American Mathematical Society, Providence (1995)

  14. Hale, J., Lunel, S.M.V.: Introduction to functional differential equations. In: Applied Mathematical Sciences, vol. 99, Springer, New York (1993)

  15. Smith, H.L.: An Introduction to Delay Differential Equations with Applications to the Life Sciences. Springer, New York (2011)

    Book  MATH  Google Scholar 

  16. Wang, W.: The exponential convergence for a delay differential neoclassical growth model with variable delay. Nonlinear Dyn. 86(3), 1875–1883 (2016)

    Article  MathSciNet  Google Scholar 

  17. Jia, R., Long, Z., Yang, M.: Delay-dependent criteria on the global attractivity of Nicholsonś blowflies model with patch structure. Math. Methods Appl. Sci. (2016). doi:10.1002/mma.4299

  18. Long, Z., Wang, W.: Positive pseudo almost periodic solutions for a delayed differential neoclassical growth model. J. Differ. Equ. Appl. 22(12), 1893–1905 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author wish to thank the anonymous reviewers whose valuable comments and suggestions led to significant improvement of the manuscript. Also, I would like to express the sincere appreciation to Prof. Jianli Li (Hunan Nomal University, Changsha, China) for the helpful discussion when this work was being carried out. This work was supported by the Scientific Research Foundation of Hunan Provincial Education Department (Grant No. 13A093), and the “Twelfth five-year” education scientific planning project of Hunan province (XJK014CGD084).

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  1. School of Mathematics Finance Xiangnan, University Chenzhou, Hunan, 423000, People’s Republic of China

    Yanli Xu

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  1. Yanli Xu
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Correspondence to Yanli Xu.

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Xu, Y. New result on the global attractivity of a delay differential neoclassical growth model. Nonlinear Dyn 89, 281–288 (2017). https://doi.org/10.1007/s11071-017-3453-x

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  • DOI: https://doi.org/10.1007/s11071-017-3453-x

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