Imitation games: Power-law sensitivity to initial conditions and nonextensivity

We 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 $z.\mathrm{}$ We obtained $q\simeq -0.69$ and $z\simeq 1.32$ for the mean-field-type calculation $(d=\infty )$ and $q\simeq -0.39$ and $z\simeq 1.12$ for a square lattice $\mathrm{}(d=2\mathrm{})\mathrm{}$ 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 $d=1,2,\infty .$