Doubly diversity-induced resonance.

The influence of variability on the response of a net of bistable FitzHugh-Nagumo elements to a weak signal is investigated. The response of the net undergoes a resonancelike behavior due to additive variability. For an intermediate strength of additive variability the external signal is optimally enhanced in the output of the net (diversity-induced resonance). Furthermore, we show that additive noise strongly influences the diversity-induced resonance. Afterwards the interplay of additive and multiplicative variability on the response of the net is investigated. Starting with asymmetric bistable elements the enhancement of the signal is not very pronounced in the presence of additive variability. Via symmetry restoration by multiplicative variability the resonance is further enhanced. We call this phenomenon doubly diversity-induced resonance, because the interplay of both, additive and multiplicative variability, is essential to achieve the optimal enhancement of the signal. The restoration of symmetry can be explained by a systematic effect of the multiplicative variability, which changes the thresholds for the transitions between the two stable fixed points. We investigate the response to variability for globally and diffusively coupled networks and in dependency on the coupling strength.