Figure 1

Trajectories of the globally coupled Brusselators given by Eqs. (13) and (14) with $N=200,A=1,B_{\mathrm{av}}=2.2(>B_c),\gamma =0.5$, and $r=0.3$. For clarity, trajectories of only 20 oscillators ($j=1,11,21,...,191$) are displayed. (a) $K=0.01$, and (b) $K=50$. In (b), the limit cycle of a single Brusselator with $B=B_{\mathrm{av}}$ is also displayed with the thick line (yellow online).Reuse & Permissions

Figure 2

Aging transition boundaries for the globally coupled Brusselators (13) and (14) with $N=200,\gamma =0.5$, and $r=0.3$ for four values of $A$, as displayed. The lines show $B_{\mathrm{av}}=B_c$ for each value of $A$.Reuse & Permissions

Figure 3

Behavior of the activity parameter $s$ as a function of ${\mu }_{\mathrm{av}}/{\mu }_c$ for the three different models: Globally coupled Brusselators (plus, red; $A=1,K=10$; other parameters are the same as in Fig. 2), locally coupled Brusselators (cross, green; $A=1,K=60$; other parameters are the same as in Fig. 4), and globally coupled phase oscillators (star, blue; $\gamma =0.03,K=6$; other parameters are the same as in Fig. 5). For the first two models, ${\mu }_{\mathrm{av}}=B_{\mathrm{av}},{\mu }_c=B_c=2$, while for the last, ${\mu }_{\mathrm{av}}=a_{\mathrm{av}},{\mu }_c=a_c=1$. For the globally coupled phase model, $s$ is the standard deviation of $\exp \left(i{\theta }_j\right)$ instead of ${\theta }_j$.Reuse & Permissions

Figure 4

Aging transition boundaries for the ring of Brusselators under the coupling (17) with $N=100,\gamma =0.2$, and $r=0.3$ for four values of $A$, as displayed. The lines show the predicted critical values of $B_{\mathrm{av}}$ for $K\to \infty$, i.e. $B_c$.Reuse & Permissions

Figure 5

Aging transition boundaries of the globally coupled phase oscillators (18) with $N=100$ for four values of $\gamma$, as indicated. The line is $a_{\mathrm{av}}=a_c=1$. The aging transition boundaries were located using the variance of $\exp \left(i{\theta }_j\right)$ for each $j$.Reuse & Permissions

Figure 6

Behavior of time-averaged $\sigma$ as the coupling strength $K$ is increased. (a) ${\mu }_{\mathrm{av}}>{\mu }_c$: Globally coupled Brusselators (cross, red; $A=1,B_{\mathrm{av}}=2.4,K_0=40$ with other parameters the same as in Fig. 2). Locally coupled Brusselators (star, blue; $N=10,A=1,B_{\mathrm{av}}=2.2,K_0=100$ with other parameters the same as in Fig. 4; the system size is reduced here to accelerate $\sigma$’s convergence to the $K^{-1}$ scaling regime). Globally coupled phase oscillators (square, purple; $a_{\mathrm{av}}=1.2,\gamma =0.01,K_0=20$ with other parameters the same as in Fig. 5). The curves with corresponding colors are due to the theoretical result (22). For the globally coupled phase model, $\sigma$ is computed as the standard deviation of $\exp \left(i{\theta }_j\right)$ instead of ${\theta }_j$. (b) ${\mu }_{\mathrm{av}}<{\mu }_c$: Globally coupled Brusselators ($B_{\mathrm{av}}=1.6$). Locally coupled Brusselators ($B_{\mathrm{av}}=1.7$). Globally coupled phase oscillators ($a_{\mathrm{av}}=0.8$). Other details are the same as in (a).Reuse & Permissions