Optimal signal amplification in weighted scale-free networks.

It has been revealed that un-weighted scale-free (SF) networks have an effect of amplifying weak signals [Acebrón et al., Phys. Rev. Lett. 99, 128701 (2007)]. Such a property has potential applications in neural networks and artificial signaling devices. However, many real and artificial networks, including the neural networks, are weighted ones with adaptive and plastic couplings. For this reason, here we study how the weak signal can be amplified in weighted SF networks by introducing a parameter to self-tune the coupling weights. We find that the adaptive weights can significantly extend the range of coupling strength for signal amplification, in contrast to the relatively narrow range in un-weighted SF networks. As a consequence, the effect of finite network size occurred in un-weighted SF networks can be overcome. Finally, a theory is provided to confirm the numerical results.