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Boundedness and persistence of delay differential equations with mixed nonlinearity

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  • Berezansky, Leonid
  • Braverman, Elena

Abstract

For a nonlinear equation with several variable delays x˙(t)=∑k=1mfk(t,x(h1(t)),⋯,x(hl(t)))−g(t,x(t)),where the functions fk increase in some variables and decrease in the others, we obtain conditions when a positive solution exists on [0, ∞), as well as explore boundedness and persistence of solutions. Finally, we present sufficient conditions when a solution is unbounded. Examples include the Mackey–Glass equation with non-monotone feedback and two variable delays; its solutions can be neither persistent nor bounded, unlike the well studied case when these two delays coincide.

Suggested Citation

  • Berezansky, Leonid & Braverman, Elena, 2016. "Boundedness and persistence of delay differential equations with mixed nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 154-169.
    • Handle: RePEc:eee:apmaco:v:279:y:2016:i:c:p:154-169
    DOI: 10.1016/j.amc.2016.01.015
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    References listed on IDEAS

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    1. Xia, Yonghui & Wong, Patricia J.Y., 2009. "Global exponential stability of a class of retarded impulsive differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 440-453.
    2. Győri, István & Hartung, Ferenc & Mohamady, Nahed A., 2015. "On a nonlinear delay population model," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 909-925.
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    Cited by:

    1. Teresa Faria, 2021. "Permanence for Nonautonomous Differential Systems with Delays in the Linear and Nonlinear Terms," Mathematics, MDPI, vol. 9(3), pages 1-20, January.
    2. Huang, Chuangxia & Yang, Xiaoguang & Cao, Jinde, 2020. "Stability analysis of Nicholson’s blowflies equation with two different delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 201-206.
    3. Amster, Pablo & Bondorevsky, Melanie, 2021. "Persistence and periodic solutions in systems of delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 403(C).

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