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Dynamics of Rodent Population With Two Predators

  • Haniyeh Fattahpour
  • Hamid R. Z. Zangeneh
  • Wayne Nagata
Original Paper
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Abstract

Modeling rodent populations has been always a challenge for population ecologists. These populations have oscillations that are dynamically complex. In this paper, we consider the population dynamics of rodents under the effect of the “specialist” and “generalist” predators with Beddington–DeAngelis and sigmoidal functional responses. We discover that the ODE system has one axial state and two boundary states. If the rate of predation by the generalist predator is more than the critical value \((c_2>c_2^*)\), then the system has a unique internal equilibrium which is stable if the predator’s intrinsic growth rate of population is more than the critical value \(s^*\). We show that the predation rates of the both predators (\(c_1, c_2\)) play an important role on rodent population dynamic. Then, we have considered a delay differential equation (DDE) model to account for the time delays in the transient dynamics. By treating time delays as the bifurcation parameter, we show that a Hopf bifurcation about the equilibria could happen for critical time delays. Finally, we gave an biological interpretation of our analytical results.

Keywords

Rodent population Specialist and generalist predator Delay differential equation Beddington–DeAngelis functional response Stability analysis Hopf bifurcation 

Mathematics Subject Classification

Primary 37N25 Secondary 37L10 37L15 35B10 

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  • Haniyeh Fattahpour
    • 1
  • Hamid R. Z. Zangeneh
    • 1
  • Wayne Nagata
    • 2
  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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