A second-order impact model for forest fire regimes

Detection and continuation of a border collision bifurcation in a forest fire model

“…Very recently, a simpler second-order impact model for the long-term prediction of forest fires has been proposed [12]. In this model, the vegetational growth is described by two standard ordinary differential equations (one for the surface layer (bush) and one for the upper layer (trees)), while fire episodes are modeled as instantaneous events.…”

“…The model considered in the following describes the dynamics of forest fires and its bifurcation analysis complements the simulation study carried out in [12]. As we will see, the key for understanding the transition from chaos to cycles is, indeed, a border collision bifurcation.…”

Border Collision of Non-Hyperbolic Fixed Points

“…For an example of border-fold bifurcation, we consider the forest fire impacting model presented in Maggi, 2005, Maggi andRinaldi, 2006]. The model describes the vegetational growth with the following two (smooth) ODEs:…”

“…triggering mixed fires with post-fire conditions suitably assigned as a function of pre-fire conditions (see [Maggi and Rinaldi, 2006] for more details).…”

Bifurcation analysis of piecewise smooth ecological models

“…Impact models represent the most naïve approach to the description of systems characterized by dynamic phenomena occurring at very diversified time scales. The first application in ecology concerns natural forests which grows smoothly and slowly but are devastated by fire from time to time (Maggi and Rinaldi, 2006). Impact models should not be confused with an apparently similar but substantially different class of models, namely that of "periodically pulsed" systems where the discontinuity in state space is generated by a periodic exogenous shock on the system.…”