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

Published online by Cambridge University Press:  20 November 2018

Jianhong Wu  and
H. I. Freedman
Jianhong Wu
Affiliation:
Department of Mathematics, York University, North York, Ontario M3J 1P3
H. I. Freedman
Affiliation:
Applied Mathematics Institute, Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1
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Abstract

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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.

Keywords

34K2034K2534C3554H2054F2592A15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 5 , 01 October 1991 , pp. 1098 - 1120
Copyright
Copyright © Canadian Mathematical Society 1991

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