Qualitative Analysis of Three-Dimensional Single Food-Chain Model with Variable Consumption Rate in Chemostat

Abstract:

The paper studies three-dimensional food-chain model with variable consumption rate in Chemostat. Assume the prey population's consumption rate of the nutrients is quadratic function, and the predator's consumption rate of the prey population is linear function. Use qualitative theory of ordinary differential equation to analyze the equilibrium solution of the model, especially the existence and stability of positive equilibrium solutions and Hopf bifurcation solutions. Finally,several numerical simulations illustrating the theoretical analysis are also given.

• Periodical: Advanced Materials Research (Volumes 955-959)
• Pages: 463-470
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.955-959.463
• Online since: June 2014
• Authors: Jing Liu, Hong Wei Jiang, Chao Liu
• Keywords: Chemostat, Equilibrium Point, Food-Chain Model, Hopf Bifurcation, Stability

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