Diversity-induced resonance in weighted Barabási–Albert networks (Ref. 40), , . (a) and (b) show the spectral amplification factor as a function of diversity for different values of weighting parameter . (a) A weak overall coupling of . (b) A strong overall coupling of . The inset of (b) shows the differences in positions and values of the maxima more clearly. (c) The contour plot of maximum signal amplification factor on the parameter plane . Each cross marks the optimal weighting parameter for a given overall coupling strength . Each circle marks the optimal coupling strength for a given weighting parameter . (d) The optimal diversity as a function of for different values of and the optimal coupling strength .
Diversity-induced resonance on a wheel-like network consisting of a hub node and 99 fringe nodes. (a) Time traces of the hub node and the average of the fringe nodes , respectively. A phase shift take places between them. The insets show the phase shift more clearly during the two successive jumping events, respectively. (b) Phase plot of and . The upper part is the time period from 728 to 732, corresponding to the lower-left inset of (a). The lower part is the time period from 843 to 847, corresponding to the upper-right inset of (a). The phase plot crosses x-axis first at , crosses y-axis later at .
The contour plot of maximum signal amplification factor on the parameter plane calculated according to Eq. (1). The network and the parameters are the same as that in Fig. 2. Each cross marks the optimal weighting parameter for a given coupling strength . The solid line is the analytical result of Eq. (8).
Forehead-laggard relation between the hub node and its neighboring set on a BA network. (a) Time traces of the hub node and its neighboring set . The arrows indicate leave for the other fixed point ahead of . (b) Time traces of the velocities and . (c) Three separated parts of . . represents the bistable oscillation function . is the part induced by the couplings. represents the part caused by an external signal . Since is subthreshold, the jump events will not occur without the phase-shift-induced driving force. The parameters are chosen as . The degree of the hub is 175.
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