The properties of the adaptive search with different value of the parameter <i>C</i> in (7).

<p>The properties of the adaptive search with different value of the parameter <i>C</i> in (7).</p

The relationship between activity, correlation time and power law exponent.

<p>(a) Correlation time <i>t_rz</i> versus the activity <i>A</i>(<i>t</i>) (b) Exponent <i>μ</i> versus the activity <i>A</i>(<i>t</i>). For clarity, the activity is plotted in a log scale.</p

The properties of Lévy Walks, Brownian walks and the adaptive search in a patchy environment.

<p>The properties of Lévy Walks, Brownian walks and the adaptive search in a patchy environment.</p

Model of Lévy and Brownian Walks Under Different Target Densities Based on Biological Fluctuation.

<p>Variable “<i>x</i>” represents fluctuation of internal variable like the pohosporylated protein in <i>Escherichia coli</i>. The center figure is a probabilistic state machine between <i>S</i> = swimming and <i>T</i> = tumbling mode that represents motion of moving forward and change direction randomly, where <i>P</i> is a function of <i>x</i>. The activity indicates whether the current searching behavior is suited to the current target density, affecting fluctuation of <i>x</i>.</p

The corresponding Log-log histogram.

<p>Log-log histogram and the approximated fitted line of normalized flight lengths frequency <i>N(l)</i> versus the flight lengths <i>l</i> for each activity value shown in Figure 6.</p

The corresponding trajectory examples.

<p>The figure also shows the values of the activity with the average calculated value of exponent <i>μ</i>, along with the corresponding target density if the activity function is designed such that the activity value is be proportional to the to the target density.</p

Model of <i>Escherichia coli</i> motion.

<p>(a) The two basic modes (b) A biased random walks with attractant, and random walks without any (c) The energy barrier model of switching probability between the two modes without attractant.</p

The Lévy and Brownian walks pattern found in <i>Oxyrrhis Marina</i> under different prey (<i>Rhodomonas</i> sp.) densities reported in [7].

*<p>(‘/’ separates the different results between the first and second experiment performed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0016168#pone.0016168-Bartumeus1" target="_blank">[7]</a>).</p

Examples of the realized trajectories in a patchy environment.

<p>(a) Lévy Walks (I) (b) Brownian Walks (III) (c) Adaptive search.</p

The simulation screenshot for the patchy environment.

<p>(a) From a usual scale, and (b) The zoomed-in condition when the animal enters a patch of targets.</p