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1 results

  • Monotone Semiflows Generated by Neutral Functional Differential Equations With Application to Compartmental Systems

  • Jianhong Wu, H. I. Freedman
  • Journal:
    Canadian Journal of Mathematics / Volume 43 / Issue 5 / 01 October 1991
    Published online by Cambridge University Press:
    20 November 2018, pp. 1098-1120
    Print publication:
    01 October 1991
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  • This paper is devoted to the machinery necessary to apply the general theory of monotone dynamical systems to neutral functional differential equations. We introduce an ordering structure for the phase space, investigate its compatibility with the usual uniform convergence topology, and develop several sufficient conditions of strong monotonicity of the solution semiflows to neutral equations. By applying some general results due to Hirsch and Matano for monotone dynamical systems to neutral equations, we establish several (generic) convergence results and an equivalence theorem of the order stability and convergence of precompact orbits. These results are applied to show that each orbit of a closed biological compartmental system is convergent to a single equilibrium.