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Permanence for Nonautonomous Differential Systems with Delays in the Linear and Nonlinear Terms

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  • Teresa Faria

    (Departamento de Matemática and CMAFCIO, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal)

Abstract

In this paper, we obtain sufficient conditions for the persistence and permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed delays in both the linear and nonlinear terms, and where typically the nonlinear terms are nonmonotone. Applications to systems inspired by mathematical biology models are given.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:263-:d:488935
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    References listed on IDEAS

    as
    1. Berezansky, Leonid & Diblík, Josef & Svoboda, Zdeněk & Šmarda, Zdeněk, 2018. "Exponential stability of linear delayed differential systems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 474-484.
    2. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
    3. 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.
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