Ratio-dependent predator-prey models of interacting populations

Research output: Journal PublicationArticlepeer-review

130 Citations (Scopus)


Ratio-dependent predator-prey models are increasingly favored by both the theoretical and experimental ecologists as a more suitable alternative to describe predator-prey interactions when the predators hunt seriously. In this article, the classical Bazykin's model is modified with ratio-dependent functional response. Stability and bifurcation situations of the system are observed. Since the ratio-dependent model always has difficult dynamics in the vicinity of the origin, the analytical behavior of the system near origin is studied completely. It is found that paradox of enrichment can happen to this system under certain parameter values, although the functional response is ratio-dependent. The parametric space for Turing spatial structure is determined. We also conclude that competition among the predator population might be beneficial for predator species under certain circumstances. Finally, ecological interpretations of our results are presented in the discussion section.

Original languageEnglish
Pages (from-to)430-452
Number of pages23
JournalBulletin of Mathematical Biology
Issue number2
Publication statusPublished - Feb 2009
Externally publishedYes


  • Bifurcation
  • Competition among predators
  • Paradox of enrichment
  • Permanence
  • Predator-prey
  • Ratio-dependence
  • Stability

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry,Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


Dive into the research topics of 'Ratio-dependent predator-prey models of interacting populations'. Together they form a unique fingerprint.

Cite this