Prey-predator models with variable carrying capacity

Mariam K.A. Al-Moqbali, Nasser Al-Salti, Ibrahim M. Elmojtaba

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Prey-predator models with variable carrying capacity are proposed. These models are more realistic in modeling population dynamics in an environment that undergoes changes. In particular, prey-predator models with Holling type I and type II functional responses, incorporating the idea of a variable carrying capacity, are considered. The carrying capacity is modeled by a logistic equation that increases sigmoidally between an initial value k0 > k1 (a lower bound for the carrying capacity) and a final value k1 + k2 (an upper bound for the carrying capacity). In order to examine the effect of the variable carrying capacity on the prey-predator dynamics, the two models were analyzed qualitatively using stability analysis and numerical solutions for the prey, and the predator population densities were obtained. Results on global stability and Hopf bifurcation of certain equilibrium points have been also presented. Additionally, the effect of other model parameters on the prey-predator dynamics has been examined. In particular, results on the effect of the handling parameter and the predator's death rate, which has been taken to be the bifurcation parameter, are presented.

Original languageEnglish
Article number102
JournalMathematics
Volume6
Issue number6
DOIs
Publication statusPublished - Jun 15 2018

Keywords

  • Hopf bifurcation
  • Limit cycle
  • Prey-predator
  • Variable carrying capacity

ASJC Scopus subject areas

  • Mathematics(all)

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