اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn impulsive modelling framework of fire occurrence in a size structured model of tree-grass interactions for savanna ecosystems
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Fires and rainfall are major mechanisms that regulate woody and grassy biomasses in savanna ecosystems. Conditions of long-lasting coexistence of trees and grasses have been mainly studied using continuous-time modelling of tree-grass competition. In these frameworks, fire is a time-continuous forcing while the relationship between woody plant size and fire-sensitivity is not systematically considered. In this paper, we propose a new mathematical framework to model tree-grass interaction that takes into account both the discrete nature of fire occurrence and size-dependent fire sensitivity (via two classes of woody plants). We carry out a qualitative analysis that highlights ecological thresholds and bifurcations parameters that shape the dynamics of the savanna-like systems within the main ecological zones. Moreover, through a qualitative analysis, we show that the impulsive modelling of fire occurrences leads to more diverse behaviors and a more realistic array of solutions than the analogous time-continuous fire models. Numerical simulations are provided to illustrate the theoretical results and to support a discussion about the bifurcation parameters and future developments.
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Many systems in life sciences have been modeled by reaction-diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events, etc) such
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