State-dependent fire models and related renewal processes

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 4, 2006, Pages

  Daly, Edoardo ^a   Porporato, Amilcare ^a  

^a Duke University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; ECOSYSTEMS; GAUSSIAN NOISE (ELECTRONIC); NEUROLOGY; PROBABILISTIC LOGICS; PROBABILITY DISTRIBUTIONS;

DEGREES OF COMPLEXITY; INTERFIRE STATISTICS; MULTIPLICATIVE NOISE;

RANDOM PROCESSES;

EID: 33750164890     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.041112     Document Type: Article

References (34)

1. A. Schenzle and H. Brand, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.20.1628 20, 1628 (1979).
2. N. G. Van Kampen, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01007642 24, 175 (1981).
3. W. Horsthemke and R. Lefever, Noise-Induced Transitions. Theory and Applications in Physics, Chemistry, and Biology (Springer-Verlag, Berlin, 1984).
4. C. R. Doering, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(87)90791- 2 122, 133 (1987).
5. C. Gardiner, Handbook of Stochastic Processes (Springer-Verlag, Berlin, 1989).
6. S. I. Denisov and W. Horsthemke, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.031105 65, 031105 (2002).
7. S. I. Denisov and W. Horsthemke, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.061109 65, 061109 (2002).
8. A. Porporato and P. D'Odorico, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.110601 92, 110601 (2004).
9. P. D'Odorico, F. Laio, and L. Ridolfi, Am. Nat. AMNTA4 0003-0147 167, E79 (2006).
10. D. R. Cox, Renewal Theory (Methuen, London, 1962).
11. E. Parzen, Stochastic Processes (Holden Day, San Francisco, 1962).
12. O. Kella, D. Perry, and W. Stadje, Probab. Eng. Inf. Sci. 17, 1 (2003).
13. F. B. Hanson and H. C. Tuckwell, Theor Popul. Biol. ZZZZZZ 0040-5809 19, 1 (1981).
14. G. L. Gerstein and B. Mandelbrot, Biophys. J. BIOJAU 0006-3495 4, 41 (1964).
15. A. V. Holden, Models of the Stochastic Activity of Neurons (Springer-Verlag, Berlin, 1976).
16. H. C. Tuckwell, Introduction to Theoretical Neurobiology. II. Nonlinear and Stochastic Theories (Cambridge University Press, Cambridge, England, 1988).
17. M. J. Chacron, B. Lindner, and A. Longtin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.080601 92, 080601 (2004).
18. B. Lindner, M. J. Chacron, and A. Longtin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.021911 72, 021911 (2005).
19. B. Lindner and A. Longtin, J. Theor. Biol. JTBIAP 0022-5193 232, 505 (2005).
20. J. S. Clark, Oikos OIKSAA 0030-1299 56, 17 (1989).
21. E. A. Johnson and S. L. Gustell, Adv. Ecol. Res. 25, 239 (1994).
22. J. M. Briggs and A. K. Knapp, Am. J. Bot. AJBOAA 0002-9122 82, 1024 (1995).
23. D. R. Cox and H. D. Miller, The Theory of Stochastic Processes (Methuen, London, 1965).
24. H. C. Tuckwell and F. Y. M. Wan, J. Appl. Probab. JPRBAM 0021-9002 21, 695 (1984).
25. E. Daly and A. Porporato, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.026108 73, 026108 (2006).
26. D. Sornette, Critical Phenomena in Natural Sciences, 2nd ed. (Springer-Verlag, Berlin, 2004).
27. N. T. Kottegoda and R. Rosso, Statistics, Probability, and Reliability for Civil and Environmental Engineeers (McGraw-Hill, Singapore, 1997).
28. A.-L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/nature03459 435, 207 (2005).
29. A. Vázquez, J. G. Oliveira, Z. Dezsö, K. I. Goh, I. Kondor, and A.-L. Barabasi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.036127 73, 036127 (2006).
30. A. Vázquez, e-print physics/0603064, Physica A (to be published).
31. A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions of Ordinary Differential Equations (CRC Press, Boca Raton, 1995).
32. Handbook of Mathematical Functions, edited by, M. Abramowitz, and, I. A. Stegun, (Dover, New York, 1965).
33. A. D. Polyanin, Handbook for Linear Partial Differential Equations for Engineers and Scientists (CRC Press, Boca Raton, 2002).
34. J. Ockendon, S. Howison, A. Lacey, and A. Movchan, Applied Partial Differential Equations (Oxford University Press, Oxford, 1999).