Conference on Computational Physics
Transcrição
Conference on Computational Physics
Conference on Computational Physics - 2008 LYAPUNOV EXPONENTS OF THE GENERALIZED LOGISTIC MAP B. C. T. Cabella† , A. L. Espı́ndola, A. S. Martinez Departamento de Fı́sica e Matemática, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo. E-mail: [email protected] Recently, the generalization of the logarithmic and exponential functions has attracted the attention of researches. One-parameter generalization of logarithmic and exponential functions have been proposed [1, 2, 3, 4, 5]. A particular one-parameter generalization of the logarithm and exponential function, based only in geometric arguments coincide with the ones of non-extensive statistical mechanics. They are suitable to unify the most of the popular one-specie continuous and discrete population dynamics models into simple formulas [6, 7, 8, 9, 10]. In this work we discretize the Richards’ model that is suitably written in terms of the generalized logarithm function and generalizes the Verhulst and Gompetz models. From this discretization, one obtains a generalized logistic map. This map presents a route to chaos similar to the logistic map but with different Lyapunov constants. We present the numerical calculation of these constants and discuss the universality class this generalized logistic maps that it belongs. [1] C. Tsallis, J. Stat. Phys. 52, 479 (1998). [2] C. Tsallis, Quim. Nova 17, 468 (1994). [3] L. Nivanem et al., Rep. Math. Phys. 52, 437 (2003). [4] E. P. Borges, Physica A 340, 95 (2004). [5] N. Kalogeropoulos, Physica A 356, 408 (2005). [6] C. Tsallis et al., Physica A 233, 395 (1996). [7] D. O. Cajueiro, Physica A 364, 385 (2006). [8] D. O. Cajueiro et al., Physica A 373, 593 (2007). [9] C. Anteneodo et al., Europhys. Lett. 59, 635 (2002). [10] A. de Jesus Holanda et al., Physica A 344, 530 (2004).