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2005, Volume 12, Issue 3: 481-500. Doi: 10.3934/dcds.2005.12.481
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On a generalized Yorke condition for scalar delayed population models

  • 1.

    Departamento de Matemática, Faculdade de Ciências, and CMAF, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa

  • 2.

    Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación, Universidad de Vigo, Campus Marcosende, 36280 Vigo

  • 3.

    Departamento de Matemática, and CMAT, Universidade do Minho, Campus de Gualtar, 4710-057 Braga

  • 4.

    Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca

Received:  September 30, 2003
Revised:  June 30, 2004
Published:  March 2005
Abstract Related Papers Cited by
    Abstract
  • For a scalar delayed differential equation $\dot x(t)=f(t,x_t)$, we give sufficient conditions for the global attractivity of its zero solution. Some technical assumptions are imposed to insure boundedness of solutions and attractivity of non-oscillatory solutions. For controlling the behaviour of oscillatory solutions, we require a very general condition of Yorke type, together with a 3/2-condition. The results are particularly interesting when applied to scalar differential equations with delays which have served as models in populations dynamics, and can be written in the general form $\dot x(t)=(1+x(t))F(t,x_t)$. Applications to several models are presented, improving known results in the literature.
    Mathematics Subject Classification: 34K20, 34K25.

    Citation:
    shu

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