Research article

Asymptotic behavior for a class of population dynamics

  • Received: 06 February 2020 Accepted: 19 March 2020 Published: 01 April 2020
  • MSC : 34C25, 34K13, 34K25

  • This paper investigates the asymptotic behavior for a class of n-dimensional population dynamics systems described by delay differential equations. With the help of technique of differential inequality, we show that each solution of the addressed systems tends to a constant vector as t → ∞, which includes many generalizations of Bernfeld-Haddock conjecture. By the way, our results extend some existing literatures.

    Citation: Chuangxia Huang, Luanshan Yang, Jinde Cao. Asymptotic behavior for a class of population dynamics[J]. AIMS Mathematics, 2020, 5(4): 3378-3390. doi: 10.3934/math.2020218

    Related Papers:

  • This paper investigates the asymptotic behavior for a class of n-dimensional population dynamics systems described by delay differential equations. With the help of technique of differential inequality, we show that each solution of the addressed systems tends to a constant vector as t → ∞, which includes many generalizations of Bernfeld-Haddock conjecture. By the way, our results extend some existing literatures.
    加载中


    [1] D. Yang, X. Li, J. Qiu, Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback, Nonlinear Anal. Hybrid Syst., 32 (2019), 294-305. doi: 10.1016/j.nahs.2019.01.006
    [2] X. Yang, X. Li, Q. Xi, et al. Review of stability and stabilization for impulsive delayed systems, Math. Biosci. Eng., 15 (2018), 1495-1515. doi: 10.3934/mbe.2018069
    [3] X. Li, X. Yang, T. Huang, Persistence of delayed cooperative models: Impulsive control method, Appl. Math. Comput., 342 (2019), 130-146.
    [4] Y. Tan, C. Huang, B. Sun, et al. Dynamics of a class of delayed reaction-diffusion systems with Neumann boundary condition, J. Math. Anal. Appl., 458 (2018), 1115-1130. doi: 10.1016/j.jmaa.2017.09.045
    [5] C. Huang, X. Long, J. Cao, Stability of anti-periodic recurrent neural networks with multiproportional delays, Math. Method Appl. Sci., 2020.
    [6] J. Zhang, C. Huang, Dynamics analysis on a class of delayed neural networks involving inertial terms, Adv. Differ. Equations, 120 (2020), 1-12.
    [7] X. Long, S. Gong, New results on stability of Nicholson's blowflies equation with multiple pairs of time-varying delays, Appl. Math. Lett., 100 (2020), 106027.
    [8] C. Huang, Y. Qiao, L. Huang, et al. Dynamical behaviors of a food-chain model with stage structure and time delays, Adv. Differ. Equations, 186 (2018).
    [9] C. Huang, J. Cao, F. Wen, et al. Stability Analysis of SIR Model with Distributed Delay on Complex Networks, Plos One, 11 (2016), e0158813.
    [10] H. Hu, X. Yuan, L. Huang, et al. Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks, Math. Biosci. Eng., 16 (2019), 5729-5749. doi: 10.3934/mbe.2019286
    [11] H. Hu, X. Zou, Existence of an extinction wave in the fisher equation with a shifting habitat, Proc. Am. Math. Soc., 145 (2017), 4763-4771. doi: 10.1090/proc/13687
    [12] H. Hu, T. Yi, X. Zou, On spatial-temporal dynamics of Fisher-KPP equation with a shifting environment, Proc. Amer. Math. Soc., 148 (2020), 213-221.
    [13] J. Wang, C. Huang, L. Huang, Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type, Nonlinear Anal. Hybrid Syst., 33 (2019), 162-178. doi: 10.1016/j.nahs.2019.03.004
    [14] J. Wang, X. Chen, L. Huang, The number and stability of limit cycles for planar piecewise linear systems of nodeCsaddle type, J. Math. Anal. Appl., 469 (2019), 405-427. doi: 10.1016/j.jmaa.2018.09.024
    [15] C. Huang, Z. Yang, T. Yi, et al. On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities, J. Differ. Equations, 256 (2014), 2101-2114. doi: 10.1016/j.jde.2013.12.015
    [16] C. Huang, H. Zhang, J. Cao, et al. Stability and Hopf bifurcation of a delayed prey-predator model with disease in the predator, Int. J. Bifurcation Chaos, 29 (2019), 1950091.
    [17] C. Huang, H. Zhang, L. Huang, Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term, Commun. Pure Appl. Anal., 18 (2019), 3337-3349. doi: 10.3934/cpaa.2019150
    [18] C. Qian, Y. Hu, Novel stability criteria on nonlinear density-dependent mortality Nicholson's blowflies systems in asymptotically almost periodic environments, J. Inequal. Appl., 13 (2020), 1-18.
    [19] C. Huang, X. Long, L. Huang, et al. Stability of almost periodic Nicholson's blowflies model involving patch structure and mortality terms, Can. Math. Bull., (2019), 1-18.
    [20] C. Huang, H. Yang, J. Cao, Weighted Pseudo Almost Periodicity of Multi-Proportional Delayed Shunting Inhibitory Cellular Neural Networks with D operator, Discrete Contin. Dyn. Syst. Ser. S, 2020.
    [21] S. R. Bernfeld, J. R. A. Haddock, A variation of Razumikhin's method for retarded functional equations, In: Nonlinear systems and applications, An International Conference, New York: Academic Press, 1977, 561-566.
    [22] C. Jehu, Comportement asymptotique des solutions de equation x'(t) = -f (t, x(t)) + f (t, x(t - 1)) + h(t) (in French), Ann. Soc. Sci. Brux. I, 92 (1979), 263-269.
    [23] T. Ding, Asymptotic behavior of solutions of some retarded differential equations, Sci. China Ser. A-Math., 25 (1982), 363-371.
    [24] T. Yi, L. Huang, Asymptotic behavior of solutions to a class of systems of delay differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 1375-1384. doi: 10.1007/s10114-005-0932-7
    [25] M. Xu, W. Chen, X. Yi, New generalization of the two-dimensional Bernfeld-Haddock conjecture and its proof, Nonlinear Anal. Real World Appl., 11 (2010), 3413-3420. doi: 10.1016/j.nonrwa.2009.12.001
    [26] Q. Zhou, W. Wang, Q. Fan, A generalization of the three-dimensional Bernfeld-Haddock conjecture and its proof, J. Comput. Appl. Math., 233 (2009), 473-481. doi: 10.1016/j.cam.2009.07.047
    [27] B. S. Chen, Asymptotic behavior of solutions of some infinite retarded differential equations(in Chinese), Acta Math. Sin. (Engl. Ser.), 3 (1990), 353-358.
    [28] T. Ding, Applications of the qualitative methods in ordinary differential equations (in Chinese), Peking: China Higher Education Press, 2004, 155-163.
    [29] T. Yi, L. Huang, Convergence of solution to a class of systems of delay differential equations, Nonlinear Dyn. Syst. Theory, 5 (2005), 189-200.
    [30] Q. Zhou, Convergence for a two-neuron network with delays, Appl. Math. Lett., 22 (2009), 1181-1184. doi: 10.1016/j.aml.2009.01.028
    [31] S. Hu, L. Huang, T. Yi. Convergence of bounded solutions for a class of systems of delay differential equations, Nonlinear Anal., 61 (2005), 543-549.
    [32] B. S. Chen, Asymptotic behavior of a class of nonautonomous retarded differential equations (in Chinese), Chinese Sci. Bull., 6 (1988), 413-415.
    [33] T. Yi, L. Huang, Convergence for pseudo monotone semi-flows on product ordered topological spaces, J. Differ. Equations, 214 (2005), 429-456. doi: 10.1016/j.jde.2005.02.005
    [34] Q. Zhou, Asymptotic behavior of solutions to a first-order non-homogeneous delay differential equation, Electron. J. Differ. Equations, 103 (2011), 1-8.
    [35] B. Liu, Asymptotic behavior of solutions to a class of non-autonomous delay differential equations, J. Math. Anal. Appl., 446 (2017), 580-590. doi: 10.1016/j.jmaa.2016.09.001
    [36] B. Liu, A generalization of the Bernfeld-Haddock conjecture, Appl. Math. Lett., 65 (2017), 7-13. doi: 10.1016/j.aml.2016.09.018
    [37] S. Xiao, Asymptotic behavior of solutions to a non-autonomous system of two-dimensional differential equations, Electron. J. Differ. Equations, 2017 (2017), 1-12.

    © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
  • Reader Comments
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(215) PDF downloads(295) Cited by(9)

Article outline

Figures and Tables

Figures(2)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog