Weak signal amplification induced by oscillator diversity in a globally coupled bistable system

Neuron diversity in the brain can effectively process and amplify the signal, and enhance the response of biological systems to weak signals. Weak signal amplification in a globally coupled network of the FitzHugh-Nagumo (FHN) oscillators is investigated, where parameter diversity is introduced via Gaussian-distributed excitability with standard deviation. In addition, the proportion of negative oscillators is introduced to independently investigate how the balance between positive and negative oscillators affects signal amplification. Both the simulation results and theoretical predictions indicate that (i) there exists an optimal interval of negative oscillator proportion in the globally coupled system that makes the weak signal propagation the strongest, within which all oscillators exhibit large-amplitude oscillations, and (ii) a critical level of oscillator diversity is reached at which the propagation of weak signals is observed to transition from failure to success. This transition is associated with a change in the system's potential from a W-shaped to a U-shaped profile. Below the threshold, the oscillators are confined within a single well due to a high potential barrier, and signal amplification is suppressed. Once the threshold is exceeded, the barrier is reduced, allowing inter-well transitions through which the system's response to weak signals is enhanced. Our qualitative analysis of the oscillator diversity provides a theoretical basis for the study of signal amplification in the neural system.