Electrocommunication for weakly electric fish

Figure 3.  Before the JAR (the EOD frequencies of the two fish are the same). Plot of $ u(x) = u_1(x) + u_2(x) $, where $ u(x,t) = u(x) e^{i\omega_0 t} $

Figure 4.  After the JAR (the EOD frequencies $ \omega_1 $ and $ \omega_2 $ of the two fish are apart from each other)

Figure 1.  Standard shape of the pulse wave $ h(t) $

Figure 2.   

Figure 5.  The setting. $ \mathfrak{F}{1} $ is acquiring measurements at $ N_s = 150 $ different closely spaced positions

Figure 6.  Estimate of the position and the orientation of $ \mathfrak{F}{2} $, with noise level $ \sigma_0 = 0.1 $. The dashed red curve represents the estimated body of $ \mathfrak{F}{2} $, whereas the green one represents the true body of $ \mathfrak{F}{2} $. The white circle represents a small dielectric object placed between $ \mathfrak{F}{1} $ and $ \mathfrak{F}{2} $

Figure 7.  Plot of the imaging functional $ \mathcal{I}_2 $ that the fish $ \mathfrak{F}{1} $ uses to track $ \mathfrak{F}{2} $

Figure 8.  Plot of the linear trajectory tracking. $ N_{\text{exp}} = 10 $ trials have been considered

Figure 9.  Plot of the trajectory tracking when the leading fish is swimming in circle, clockwisely. $ N_{\text{exp}} = 10 $ trials/realizations have been considered

Figure 10.  Plot of the isopotential lines when $ \mathfrak{F}{2} $ (on the left) is passive (electrically silent) and $ \mathfrak{F}{1} $ (on the right) is active

Figure 11.  Plot of the MUSIC imaging functional used in Algorithm 3 by using $ N_r = 32 $ receptors and $ N_f = 100 $ frequencies, with noise level $ \sigma_0 = 0.1 $. The square and the diamond indicate the approximation of the center and the true center of the target D, respectively. $ \mathfrak{F}{1} $ (right) can image the target despite the presence of $ \mathfrak{F}{2} $ (left), which is estimated by applying Algorithm 2