Dynamics of the diffusive Nicholson's blowflies equation with distributed delay

S. A. Gourley, Shigui Ruan

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

In this paper we study the diffusive Nicholson's blowflies equation. Generalizing previous works, we model the generation delay by using an integral convolution over all past times and results are obtained for general delay kernels as far as possible. The linearized stability of the non-zero uniform steady state is studied in detail, mainly by using the principle of the argument. Global stability both of this state and of the zero state are studied by using energy methods and by employing a comparison principle for delay equations. Finally, we consider what bifurcations are possible from the non-zero uniform state in the case when it is unstable.

Original languageEnglish (US)
Pages (from-to)1275-1291
Number of pages17
JournalRoyal Society of Edinburgh - Proceedings A
Volume130
Issue number6
StatePublished - 2000
Externally publishedYes

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Distributed Delay
Comparison Principle
Delay Equations
Energy Method
Global Stability
Convolution
Bifurcation
Unstable
kernel
Zero
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Dynamics of the diffusive Nicholson's blowflies equation with distributed delay. / Gourley, S. A.; Ruan, Shigui.

In: Royal Society of Edinburgh - Proceedings A, Vol. 130, No. 6, 2000, p. 1275-1291.

Research output: Contribution to journalArticle

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