---
title: "Imitation Games: Power-law Sensitivity to Initial Conditions and Nonextensivity • CBPF Index"
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**Physics Note****Published**

# **Imitation Games: Power-law Sensitivity to Initial Conditions and Nonextensivity**

**A. R. R. Papa; C. Tsallis**

1997

[**Download PDF **0.3 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb511/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Imitation%20Games%3A%20Power-law%20Sensitivity%20to%20Initial%20Conditions%20and%20Nonextensivity)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>A. R. R. Papa; C. Tsallis</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>1997</dd>

<dt>Description</dt>
<dd>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 (1994), and which modelizes the battle of birds for defending their territories. From the associated exponent we obtain the value for the entropic index ''q'' which defines the recently introduced nonextensive generali- zation of the Boltzmann-Gibbs thermostatistics. In addition to that, we calculate the dynamical exponent ''z''. We obtained &lt;math&gt; q \simeq - 0.69 \,\!&lt;/math&gt; and &lt;math&gt; z \simeq 1.32 \,\!&lt;/math&gt; for a mean-field-type calculation &lt;math&gt;(d = \infty )\,\!&lt;/math&gt;, and &lt;math&gt; q \simeq - 0.39 \,\!&lt;/math&gt; and &lt;math&gt; z \simeq 1.12\,\!&lt;/math&gt; for the square lattice (d = 2).</dd>

<dt>Year</dt>
<dd>1997</dd>

<dt>Number</dt>
<dd>CBPF-NF-030/97</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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