Noise and seasonal effects on the dynamics of plant-herbivore models with monotonic plant growth functions. (English) Zbl 1247.37091

This paper considers a class of discrete-time models for the growth dynamics of a plant species and for the dynamics resulting from the interaction of one plant and one herbivore species. The growth of a single plant species is modelled by a one-dimensional map, and assumptions on the monotonicity of the functional form of the map are shown to have various dynamical consequences. The model for the interaction of plants and herbivores has one free function, and the consequences of the monotonicity of this function are investigated. The presented examples involve the maximum value of the variables as \(t\rightarrow\infty\), the number of equilibria and their stability, and the bifurcations they undergo. The results are applied to two specific models, and periodic orbits and a heteroclinic bifurcation are found. The effects of noise near the heteroclinic bifurcation are also investigated.


37N25 Dynamical systems in biology
39A28 Bifurcation theory for difference equations
39A30 Stability theory for difference equations
92B05 General biology and biomathematics
Full Text: DOI arXiv


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