Bifurcation analysis of an impact model for forest fire prediction

International Journal of Bifurcation and Chaos

Volumn 18, Issue 8, 2008, Pages 2275-2288

  Bizzarri, Federico ^a   Storace, Marco ^a   Colombo, Alessandro ^b  

^a UNIVERSITY OF GENOA   (Italy)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Bifurcation analysis; Forest fire model; Impact system; Piecewise smooth map

Indexed keywords

BIFURCATION (MATHEMATICS); DEFORESTATION; FIRE HAZARDS; FORECASTING; FORESTRY;

BIFURCATION ANALYSIS; FOREST FIRE MODEL; FOREST FIRE PREDICTION; IMPACT SYSTEM; PIECEWISE-SMOOTH MAP; QUALITATIVE BEHAVIOR; SECOND ORDERS; TWO-DIMENSIONAL FLOW;

FIRES;

CONTROL SYSTEMS; DEFORESTATION; FIRES; FORECASTS; FOREST FIRES; MATHEMATICAL MODELS; MATHEMATICS; NONLINEAR PROGRAMING; PARAMETERS;

EID: 54949090760     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127408021701     Document Type: Article

References (18)

1. Banerjee, S., Karthik, M. S., Yuan, G. & Yorke, J. A. [2000a] "Bifurcations in one-dimensional piecewise smooth maps - Theory and applications in switching circuits," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 47, 389-394.
2. Banerjee, S., Ranjan, P. & Grebogi, C. [2000b] "Bifurcations in two-dimensional piecewise smooth maps - Theory and applications in switching circuits," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 47, 633-642.
3. Bizzarri, F., Storace, M., Gardini, L. & Lupini, R. [2001] "Bifurcation analysis of a PWL chaotic circuit based on hysteresis through a one-dimensional map," Int. J. Bifurcation and Chaos 11, 1911-1927.
4. Bizzarri, F. & Storace, M. [2002] "Two-dimensional bifurcation diagrams of a chaotic circuit based on hysteresis," Int. J. Bifurcation and Chaos 12, 43-69.
5. Bizzarri, F., Caruso, L. & Storace, M. [2006] "Bifurcation analysis of a second-order impact model for forest fire prediction through a 1D-map," in Proc. of ISCAS'06, Kos, Greece, 21-24 May 2006.
6. Casagrandi, R. & Rinaldi, S. [1999] "A minimal model for forest fire regimes," Am. Nat. 153, 527-539.
7. Dercole, F. & Maggi, S. [2005] "Detection and continuation of a border collision bifurcation in a forest fire model," Appl. Math. Comput. 168, 623-635.
8. Di Bernardo, M., Feigen, M. I., Hogan, S. J. & Homer, M. E. [1999] "Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems," Chaos Solit. Fract. 10, 1881-1908.
9. Halse, C., Homer, M. & Di Bernardo, M. [2003] "C- bifurcafions and period-adding in one-dimensional piecewise-smooth maps," Chaos Solit. Fract. 18, 953-976.
10. Jain, P. & Banerjee, S. [2003] "Border-collision bifurcations in one-dimensional discontinuos maps," Int. J. Bifurcation and Chaos 13, 3341-3352.
11. Kuznetsov, Y. A. [2004] Elements of Applied Bifurcation Theory. 3rd edition (Springer, NY).
12. Lupini, R., Bizzarri, F. & Storace, M. [2001] "Discontinuities in a one-dimensional map describing a hysteretic chaotic circuit," Nonlin. Anal. TMA 47, 5253-5264.
13. Maggi, S. & Rinaldi, S. [2006] "A second-order impact model for forest fire regimes," Theor. Popul. Biol. 70, 174-182.
14. Nordmark, A. B. [1991] "Non-periodic motion caused by grazing incidence in an impact oscillator," J. Sound Vibr. 145, 279-297.
15. Nusse, H. E. & Yorke, J. A. [1992] "Border-collision bifurcations including period two to period three for piecewise smooth systems," Physica D 57, 39-57.
16. Nusse, H. E. & Yorke, J. A. [1995] "Bordercollision bifurcations for piecewise smooth onedimensional maps," Int. J. Bifurcation and Chaos 5, 189-207.
17. Sushko, I., Agliari, A. & Gardini, L. [2005] "Bistability and border-collision bifurcations for a family of unimodal piece-wise smooth maps," Discr. Contin. Dyn. Systs. - Series B 5, 881-897.
18. Sushko, I., Agliari, A. & Gardini, L. [2006] "Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves," Chaos Solit. Fract. 29, 756-770.