Comparison principles for systems that embed in cooperative systems, with applications to diffusive Lotka-Volterra models

Research output: Contribution to journalReview article

9 Scopus citations

Abstract

It is shown that a class of noncooperative systems of differential equations can be embedded into larger cooperative systems. This observation is used to refine and extend known comparison principles and re-sults based on iteration from sub- and supersolutions in some noncooperative systems. An example which includes many sorts of diffusive Lotka-Volterra systems from mathematical ecology is analysed. The analysis includes criteria for the uniform persistence of the populations described by the system.

Original languageEnglish (US)
Pages (from-to)283-303
Number of pages21
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm
Volume3
Issue number3
StatePublished - Sep 1 1997

Keywords

  • Comparison Principles
  • Cooperative Systems
  • Lotka-Volterra Models
  • Monotone Flows
  • Monotone Methods
  • Non Cooperative Systems

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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