Produção Nacional
Imitation games: Power-law sensitivity to initial conditions and nonextensivity
1998; American Physical Society; Volume: 57; Issue: 4 Linguagem: Inglês
10.1103/physreve.57.3923
ISSN1538-4519
AutoresAndrés R. R. Papa, Constantino Tsallis,
Tópico(s)Ecosystem dynamics and resilience
ResumoWe exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions in the system of competing logistic maps introduced by Suzuki and Kaneko [Physica D 75, 328 (1994)], which modelizes the battle of birds defending their territories. From the associated exponent we obtain the value for the entropic index $q,$ which defines the recently introduced nonextensive generalization of the Boltzmann-Gibbs thermostatistics. In addition, we calculate the dynamical exponent $z.$ We obtained $q\ensuremath{\simeq}\ensuremath{-}0.69$ and $z\ensuremath{\simeq}1.32$ for the mean-field-type calculation $(d=\ensuremath{\infty})$ and $q\ensuremath{\simeq}\ensuremath{-}0.39$ and $z\ensuremath{\simeq}1.12$ for a square lattice $(d=2)$ model. Finally, we have generalized Suzuki and Kaneko's model, using an extended form of the logistic map, and have calculated the corresponding values of $q$ for $d=1,2,\ensuremath{\infty}.$
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