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. We obtained q similar or equal to-0.69 and z similar or equal to 1.32 for the mean-field-type calculation (d = infinity) and q similar or equal to-0.39 and z similar or equal to 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,infinity.