Stability and Hopf bifurcation of a producer-scrounger model with age-structure

We derive a producer-scrounger model with age-structure in scrounger and looks into its dynamics. Using the methods of eigenvalue analysis and Lyapunov function, we find sufficient and necessary conditions for globally asymptotical stability of extinction equilibrium and scrounger-free equilibrium. A so-called basic reproduction ratio R0$R_{0}$ was established to determine whether the scrounger is extinct or uniformly persistent. It is found that if R0>1$R_{0}>1$, the mature time τ does change the dynamical behavior of the model. We confirm that Hopf bifurcation happens if the mature time τ increases.

• Publication year

  2016

• Venue

  Advances in Difference Equations

• Publication date

  2016-09-22

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1186/S13662-016-0968-2
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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