Abstract

We formulate general plantherbivore interaction models with monotone plant growth functions (rates). We study the impact of monotone plant growth functions in general plantherbivore models on their dynamics. Our study shows that all monotone plant growth models generate a unique interior equilibrium and they are uniform persistent under certain range of parameters values. However, if the attacking rate of herbivore is too small or the quantity of plant is not enough, then herbivore goes extinct. Moreover, these models lead to noise sensitive bursting which can be identified as a dynamical mechanism for almost periodic outbreaks of the herbivore infestation. Montone and non-monotone plant growth models are contrasted with respect to bistability and crises of chaotic attractors.

Original languageEnglish (US)
Pages (from-to)255-274
Number of pages20
JournalInternational Journal of Biomathematics
Volume4
Issue number3
DOIs
StatePublished - Sep 1 2011

Keywords

  • Monotone growth models
  • NeimarkSacker bifurcation
  • bistability
  • crisis of chaos
  • heteroclinic bifurcation
  • noise bursting
  • periodic infestations
  • uniformly persistent

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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