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On a nonlinear delay population model

Author

Listed:
  • Győri, István
  • Hartung, Ferenc
  • Mohamady, Nahed A.

Abstract

The nonlinear delay differential equation x˙(t)=r(t)[g(t,xt)−h(x(t))],t≥0 is considered. Sufficient conditions are established for the uniform permanence of the positive solutions of the equation. In several particular cases, explicit formulas are given for the upper and lower limit of the solutions. In some special cases, we give conditions which imply that all solutions have the same asymptotic behavior, in particular, when they converge to a periodic or constant steady-state.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:909-925
    DOI: 10.1016/j.amc.2015.08.090
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    Cited by:

    1. Pal, D. & Mahapatra, G.S., 2016. "Effect of toxic substance on delayed competitive allelopathic phytoplankton system with varying parameters through stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 109-124.
    2. 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.
    3. 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.

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