Generalized exponential function and discrete growth models

Physica A: Statistical Mechanics and its Applications

Volumn 388, Issue 14, 2009, Pages 2922-2930

  Souto Martinez, Alexandre ^a,b   Silva González, Rodrigo ^a   Lauri Espíndola, Aquino ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b National Institute of Science and Technology for Complex Systems   (Brazil)

Author keywords

Complex systems; Nonlinear dynamics; Population dynamics (ecology)

Indexed keywords

DYNAMICS; LARGE SCALE SYSTEMS; POPULATION DYNAMICS;

DISCRETE GROWTH MODELS; DISCRETE MODELING; DISCRETIZATIONS; GENERALIZED EXPONENTIAL FUNCTIONS; PARAMETER GENERALIZATION; PHYSICAL INTERPRETATION; POPULATION DYNAMICS (ECOLOGY); RICHARDS MODELS;

EXPONENTIAL FUNCTIONS;

EID: 67349118388     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2009.03.035     Document Type: Article

References (42)

1. Tsallis C. J. Statist. Phys. 52 (1988) 479-487
2. Tsallis C. Química Nova 17 (1994) 468-471
3. Nivanen L., ~ A.L.M.A., and Wang Q.A. Rep. Math. Phys. 52 (2003) 437-444
4. Borges E.P. Physica A 340 (2004) 95-101
5. Kalogeropoulos N. Physica A 356 (2005) 408-418
6. Kaniadakis G. Physica A 296 (2001) 405-425
7. Kaniadakis G. Phys. Rev. E 66 (2002) 056125
8. Abe S. Phys. Lett. A 224 (1997) 326-330
9. Kaniadakis G., Lissia M., and Scarfone A.M. Phys. Rev. E 71 (2005) 046128
10. Kaniadakis G. Phys. Rev. E 72 (2005) 036108
11. Schwämmle V., and Tsallis C. J. Math. Phys. 48 (2007) 113301
12. Borges E.P. J. Phys. A: Math. Gen. 31 (1998) 5281-5288
13. Tsallis C., Levy S.V.F., Souza A.M.C., and Maynard R. Phys. Rev. Lett. 75 (1995) 3589-3592
14. Tsallis C., Levy S.V.F., Souza A.M.C., and Maynard R. Phys. Rev. Lett. 77 (1996) 5442 E
15. Tsallis C., and Stariolo D.A. Physica A 233 (1996) 395-406
16. Tsallis C., and de Albuquerque M.P. Eur. Phys. J. B 13 (2000) 777-780
17. Cajueiro D.O. Physica A 364 (2006) 385-388
18. Cajueiro D.O., and Tabak B.M. Physica A 373 (2007) 593-602
19. Anteneodo C., Tsallis C., and Martinez A.S. Europhys. Lett. 59 (2002) 635-641
20. de Jesus Holanda A., Pizza I.T., Kinouchi O., Martinez A.S., and Ruiz E.E.S. Physica A 344 (2004) 530-536
21. A.S. Martinez, R.S. González, C.A.S. Terçariol, Generalized exponential function and some of its applications to complex systems. arXiv:0812.3071v1[physics.data-an]
22. Arruda T.J., González R.S., Terçariol C.A.S., and Martinez A.S. Phys. Lett. A 372 (2008) 2578-2582
23. Martinez A.S., González R.S., and Terçariol C.A.S. Physica A 387 (2008) 5679-5687
24. Montroll E.W., and West B.J. On an enriched collection of stochastic processes. Fluctuation Phenomena (1979), Elsevier Science Publishers B. V., Amsterdam pp. 61-205
25. Montroll E.W., and Badger L.W. Introduction to Quantitative Aspects of Social Phenomena (1974), Gordon and Breach, New York
26. Richards F.J. J. Exp. Bot. 10 (1959) 290-300
27. Mombach J.C.M., Lemke N., Bodmann B.E.J., and Idiart M.A.P. A mean-field theory of cellular growth. Europhys. Lett. 59 6 (2002) 923-928
28. Mombach J.C.M., Lemke N., Bodmann B.E.J., and Idiart M.A.P. A mean-field theory of cellular growth. Europhys. Lett. 60 3 (2002) 489
29. Hassell M.P. J. Anim. Ecol. 45 (1975) 283-296
30. Bellows T.S. J. Anim. Ecol. 50 (1981) 139-156
31. Berryman A.A. Principles of Population Dynamics and Their Applications (1999), Thornes, Cheltenham
32. R.J.H. Beverton, H.S.J. , On the dynamics of exploited fish populations. Series 2, vol. 19, Her Majesty's Stationary Office, London
33. Maynard-Smith J., and Slatkin M. Ecology 54 (1973) 384-391
34. May R.M. Nature 261 (1976) 459-467
35. Feigenbaum M.J. J. Statist. Phys. 21 (1979) 669-706
36. Costa U.M.S., Lyra M.L., Plastino A.R., and Tsallis C. Phys. Rev. E 56 (1997) 245-250
37. Lyra M.L., and Tsallis C. Phys. Rev. Lett. 80 (1998) 53-56
38. da Silva C.R., da Cruz H.R., and Lyra M.L. Braz. J. Phys. 29 (1999) 144-152
39. F.A.B.F. de Moura, U. Tirnakli, M.L. Lyra, Phys. Rev. E 2000, 6361-6365
40. Ricker W.E. J. Fisheries Res. Board Can. 11 (1954) 559-623
41. Brännström A., and Sumpter D.J.T. Proc. Roy. Soc. B 272 1576 (2005) 2065-2072
42. Skellam J.G. Biometrika 38 (1951) 196-218