Fig. 5: Amplitude death and restoration dependence on different topological and system parameters.
From: Amplitude death and restoration in networks of oscillators with random-walk diffusion
Top panels show the dependence of the amplitude of the mean-field oscillations on the diffusion value D. Oscillation amplitude measured as the temporal standard deviation of the y variable’s mean-field, \(\sigma =\sigma (\overline{y})\). Each line corresponds to a specific topological or system parameter value. Bottom panels show heatmaps of the amplitude upon tuning the diffusion and the corresponding parameter. Results obtained with simulations of the Brusselator model in networks with N = 1000 nodes and system parameters for the reaction terms a = 0.5 and b = 1.7 unless otherwise stated. a, b Dependence of the oscillation amplitude σ on the diffusion D in a range of Erdös-Rényi (ER) networks with different average degree \(\left\langle k\right\rangle\). Values of \(\left\langle k\right\rangle\) for each curve in a are, from top to bottom, 80, 70, 60, 50, 40, 30, 20, and 10. c, d Dependence of the oscillation amplitude σ on the diffusion D for a range of Watts-Strogatz networks with average degree \(\left\langle k\right\rangle =20\) and rewiring probability p ∈ [0, 1]. Values of 1 − p for each curve in c are, from top to bottom, 1.0, 0.8, 0.6, 0.4, 0.2, and 0. e, f Dependence of the oscillation amplitude σ on the diffusion D for different values of the system parameter b with fixed a = 0.5 in a single ER networks with 〈k〉 = 20. Values of b for each curve in e are, from top to bottom, 2.2, 2.1, 2.0, 1.9, 1.8, 1.7, and 1.6.
