Optimal signal amplification in weighted scale-free networks

Diversity-induced resonance for optimally suprathreshold signals

Recent research has revealed that a system of coupled units with a certain degree of parameter diversity can generate an enhanced response to a subthreshold signal compared to that without diversity, exhibiting a diversity-induced resonance. We here show that diversity-induced resonance can also respond to a suprathreshold signal in a system of globally coupled bistable oscillators or excitable neurons, when the signal amplitude is in an optimal range close to the threshold amplitude. We find that such diversity-induced resonance for optimally suprathreshold signals is sensitive to the signal period for the system of coupled excitable neurons, but not for the coupled bistable oscillators. Moreover, we show that the resonance phenomenon is robust to the system size. Furthermore, we find that intermediate degrees of parameter diversity and coupling strength jointly modulate either the waveform or the period of collective activity of the system, giving rise to the resonance for optimally suprathreshold signals. Finally, with low-dimensional reduced models, we explain the underlying mechanism of the observed resonance. Our results extend the scope of the diversity-induced resonance effect.

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.

Signal transmission in a Y-shaped one-way chain

It has been found that noise plays a key role to improve signal transmission in a one-way chain of bistable systems [Zhang et al., Phys. Rev. E 58, 2952 (1998)]. We here show that the signal transmission can be sharply improved without the aid of noise, if the one-way chain with a single source node is changed with two source nodes becoming a Y-shaped one-way chain. We further reveal that the enhanced signal transmission in the Y-shaped one-way chain is regulated by coupling strength, and that it is robust to noise perturbation and input signal irregularity. We finally analyze the mechanism of the enhanced signal transmission by the Y-shaped structure.