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-0.69 and z1.32 for the mean-field-type calculation (d=∞) and q-0.39 and z1.12 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,∞.