Global attractivity and periodic solutions in delay-differential equations related to models in physiology and population biology

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21 Citations (Scopus)

Abstract

With appropriate assumptions, the following two general first-order nonlinear differential delay equations may be employed to describe some physiological control systems as well as some population growth processes: {Mathematical expression} and {Mathematical expression} It is assumed that g(x) is strictly increasing, g(0)=0, and each of these two equations has a unique positive steady state. Sufficient conditions are obtained for this steady state to be a global attractor (with respect to continuous positive initial functions) when f(x) is monotone or has only one hump. We also establish the global existence of periodic solutions in these equations.

Original languageEnglish (US)
Pages (from-to)205-238
Number of pages34
JournalJapan Journal of Industrial and Applied Mathematics
Volume9
Issue number2
DOIs
StatePublished - Jun 1992

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Global Attractivity
Physiology
Delay Differential Equations
Biology
Periodic Solution
Differential equations
Differential Delay Equations
Control systems
Population Growth
Growth Process
Global Attractor
Global Existence
Monotone
Strictly
Control System
First-order
Sufficient Conditions
Model

Keywords

  • global asymptotical stability
  • haematopoiesis
  • nonlinear delay equation
  • oscillation
  • periodic solutions

ASJC Scopus subject areas

  • Applied Mathematics
  • Engineering(all)

Cite this

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AB - With appropriate assumptions, the following two general first-order nonlinear differential delay equations may be employed to describe some physiological control systems as well as some population growth processes: {Mathematical expression} and {Mathematical expression} It is assumed that g(x) is strictly increasing, g(0)=0, and each of these two equations has a unique positive steady state. Sufficient conditions are obtained for this steady state to be a global attractor (with respect to continuous positive initial functions) when f(x) is monotone or has only one hump. We also establish the global existence of periodic solutions in these equations.

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