## 5 Results  
### Communication Range Dynamics  
A self-adaptive system will try to keep itself in a steady state by executing the necessary actions to achieve its predefined functionality regardless of external perturbations [33]. The goal of the self-adaptive system is therefore to reduce the impact of the external perturbations, or stimuli, in the normal operation of the system. In our case, the predefined functionality of the proposed fuzzy control-based self-adaptive system is to keep the network connectivity of a wireless sensor network using a probabilistic approach based on the number of neighbors, or node degree, of each node. The only action that a node can do at any iteration of the control loop is to increase or decrease its communication range by means of acting on its own transmission power. We can say then that the system has reached a steady state when there is no change in the transmission power of the node or even when the change is so small and smooth that it keeps the network connectivity over a minimum performance limit. Thus, to evaluate the performance of the system beyond the energy consumption and the connectivity, as analyzed in [10], here, we are going to evaluate its dynamical behavior. The dynamical behavior allows us to know how much effort is required for a self-adaptive system to reach its steady state. We can talk then about two main measures: the total number of actions performed by the self-adaptive system during the experiments and how fast it reaches a steady state, expressed as the number of iterations of the control loop required. As described previously, the only action the system does is over the transmission power, so these measurements are calculated just taking into account the changes in the transmission power, as shown in Figure 10. In any case the dynamics relative to the node degree and the connectivity are also shown in Figures 11 and 12, respectively, as they provide additional information of interest. \begin{table}
\begin{tabular}{c c c c c c c} \hline _Experiment_ & \(ND_{R}\) & \(\xi_{ND}\) & \(k_{CR}\) & \(P_{TX}\) (_dBm_) & \(J_{e}\) (_mAh_) & \(J_{e}\) \\ \hline e01 & — & — & — & \(-3\) & 4283.19 & 1.2500 \\ e02 & — & — & — & \(-15\) & 3408.00 & 13.7053 \\ e03 & 2 & 0 & 1 & — & 3921.53 & 21.6875 \\ e04 & 2 & 0 & 3 & — & 3947.76 & 12.0170 \\ e05 & 2 & 1 & 3 & — & 3639.89 & 4.3095 \\ e06 & 3 & 1 & 3 & — & 3817.46 & 7.0283 \\ e07 & 3 & 0 & 3 & — & 3846.54 & 5.5803 \\ e08 & 3 & 0 & 1 & — & 3865.22 & 10.3661 \\ e09 & 3 & 1 & 1 & — & 3798.83 & 9.4375 \\ e10 & 2 & 1 & 1 & — & 3952.63 & 24.5000 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters and results from previous work. Figure 10: Transmission power dynamics. (**a**) Experiment e03; (**b**) Experiment e04; (**c**) Experiment e05; (**d**) Experiment e06; (**e**) Experiment e07; (**f**) Experiment e08; (**g**) Experiment e09; (**h**) Experiment e10. Figure 11: Node degree dynamics. (**a**) Experiment e03; (**b**) Experiment e04; (**c**) Experiment e05; (**d**) Experiment e06; (**e**) Experiment e07; (**f**) Experiment e08; (**g**) Experiment e09; (**h**) Experiment e10. Figure 12: Packet delivery dynamics. (**a**) Experiment e03; (**b**) Experiment e04; (**c**) Experiment e05; (**d**) Experiment e06; (**e**) Experiment e07; (**f**) Experiment e08; (**g**) Experiment e09; (**h**) Experiment e10. The figure of merit calculated for the transmission power dynamics is obtained using Equation (20), where \(i\) represents the node and \(k\) the iteration. Therefore, this equation provides us with the total number of actions done on the transmission power for all of the nodes during the running of the experiment.