Positive and negative couplings perform complementary roles in the signal amplification of globally coupled bistable oscillators.

We investigate a system of globally coupled bistable oscillators subjected to a common weak signal, where the couplings are oscillator dependent with random signs: positive or negative. We find that neither purely positive nor purely negative couplings are optimal for signal amplification of the system; a mixture of both positive and negative couplings is more beneficial for the signal amplification. Our numerical results further show that different from the fully synchronous state caused by purely positive couplings or asynchronous state caused by purely negative couplings, the mixed positive and negative couplings can generate a clustering synchronous state, which allows the system to generate a resonancelike response to the weak signal, and thus, amplifies the signal. We finally propose a reduced model to analyze the mechanism underlying this resonancelike behavior, and find a complementary effect of these two types of couplings in signal amplification.