Continuous growth models in terms of generalized logarithm and exponential functions

Physica A: Statistical Mechanics and its Applications

Volumn 387, Issue 23, 2008, Pages 5679-5687

  Martinez, Alexandre Souto ^a   González, Rodrigo Silva ^a   Terçariol, César Augusto Sangaletti ^a,b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b CENTRO UNIVERSITÁRIO BARÃO DE MAUÁ   (Brazil)

Author keywords

Generalized logarithmic and exponential functions; Growth models; Marusic and Bajzer's model; Population dynamics; Richard's model; Tsoularis and Wallace's model

Indexed keywords

EXPONENTIAL FUNCTIONS; GROWTH MODELING; MICROSCOPIC MODELING; PHYSICAL INTERPRETATIONS;

ALGEBRA;

EID: 48749126777     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2008.06.015     Document Type: Review

References (38)

1. Tsallis C. What are the numbers experiments provide?. Química Nova 17 6 (1994) 468-471
2. Nivanen L., ~ A.L.M.A., and Wang Q.A. Generalized algebra within a nonextensive statistics. Rep. Math. Phys. 52 3 (2003) 437-444
3. Borges E.P. A possible deformed algebra and calculus inspired in nonextensive thermostatistics. Physica A 340 (2004) 95-101
4. Kalogeropoulos N. Algebra and calculus for Tsallis thermo-statistics. Physica A 356 (2005) 408-418
5. Kaniadakis G. Non-linear kinetics underlying generalized statistics. Physica A 296 3-4 (2001) 405-425
6. Kaniadakis G. Statistical mechanics in the context of special relativity. Phys. Rev. E 66 5 (2002) 056125
7. Abe S. A note on the q-deformation-theoretic aspect of the generalized entropies in nonextensive physics. Phys. Lett. A 224 (1997) 326
8. Kaniadakis G., Lissia M., and Scarfone A.M. Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics. Phys. Rev. E 71 4 (2005) 046128
9. Kaniadakis G. Statistical mechanics in the context of special relativity. II. Phys. Rev. E 72 (2005) 036108
10. Takahashi T., Oono H., and Radford M.H. Psychophysics of time perception and intertemporal choice models. Physica A 387 8-9 (2008) 2066-2074
11. Takahashi T. A comparison between Tsalliss statistics-based and generalized quasi-hyperbolic discount models in humans. Physica A 387 1-2 (2008) 551-556
12. Takahashi T. A comparison of intertemporal choices for oneself versus someone else based on Tsallis statistics. Physica A 385 2 (2007) 637-644
13. Takahashi T., Oono H., and Radford M.H. Empirical estimation of consistency parameter in intertemporal choice based on Tsallis statistics. Physica A 381 (2007) 338-342
14. Cajueiro D.O. A note on the relevance of the q-exponential function in the context of intertemporal choices. Physica A 364 (2006) 385-388
15. Takahashi T. A probabilistic choice model based on Tsallis statistics. Physica A 386 1 (2007) 335-338
16. Anteneodo C., Tsallis C., and Martinez A.S. Risk aversion in trade transactions. Europhys. Lett. 59 5 (2002) 635-641
17. de~Jesus~Holanda A., Pizza I.T., Kinouchi O., Martinez A.S., and Ruiz E.E.S. Thesaurus as a complex network. Physica A 344 3-4 (2004) 530-536
18. Tsallis C., and de Albuquerque M.P. Are citations of scientific papers a case of nonextensivity?. Eur. Phys. J. B 13 (2000) 777-780
19. Tsoularis A., and Wallace J. Analysis of logistic growth models. Math Biosci. 179 1 (2002) 21-55
20. Murray J.D. Mathematical Biology: An Introduction. 3rd edition (2002), Springer Verlag, New York
21. Boyce W.E., and DiPrima R.C. Elementary Differential Equation and Boundary Value Problem. seventh edn (2001), John Wiley & Sons, New York
22. Richards F.J. A flexible growth functions for empirical use. J. Exp. Bot. 10 (1959) 290-300
23. Spencer R.P., and Coulombe M.J. Quantification of hepatic growth and regeneration. Growth 30 (1966) 277
24. Blumberg A.A. Logistic growth rate functions. J. Theoret. Biol. 21 (1968) 42
25. Turner M.E., Bradley E.L., Kirk K.A., and Pruitt K.M. Theory of growth. Math. Biosci. 29 (1976) 367-373
26. Marusic M., and Bajzer Z. Generalized two-parameter equation of growth. J. Math. Anal. Appl. 179 (1993) 446-462
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 (2002) 923-928
28. Arruda T.J., González R.S., Terçariol C.A.S., and Martinez A.S. Arithmetical and geometrical means of generalized logarithmic and exponential functions: generalized sum and product operators. Phys. Lett. A 372 (2008) 2578-2582
29. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52 (1988) 479
30. Montroll E.W., and West B.J. On an enriched collection of stochastic processes. Fluctuation Phenomena (1979), Elsevier Science Publishers B. V, Amsterdam 61-205
31. Montroll E.W., and Badger L.W. Introduction to Quantitative Aspects of Social Phenomena (1974), Gordon and Breach, New York
32. Tsallis C., Bemski G., and Mendes R.S. Is re-association in folded proteins a case of nonextensivity?. Phys. Lett. A 257 (1999) 93-98
33. Montemurro M.A. A generalization of the Zipf-Mandelbrot law in linguistics. Nonextensive Entropy: Interdisciplinary Applications, Vol. Santa Fe Institute Studies in the Science of Complexity (2004), Oxford Publisher Press, New York 347-356
34. A.S. Martinez, R.S. González, A.L. Espíndola, Generalized exponential function and discrete growth models. 2008. arxiv:0803.3089[physics.bio-ph]
35. Niven R.K. q-Exponential structure of arbitrary-order reaction kinetics. Chem. Eng. Sci. 61 (2006) 3785-3790
36. von Bertalanffy L. Quantitative laws in metabolism and growth. Quart. Rev. Biol. 32 (1957) 217-231
37. Savageau M.A. Allometric morphogenesis of complex systems: Derivation of the basic equations form first principles. Proc. Natl. Acad. Sci. USA 76 (1979) 6023-6025
38. Savageau M.A. Growth equations: A general equations and a survey of special cases. Math. Biosci. 48 (1980) 267-278